Jul 7, 2018 - 3.1.3.7 Pull-outtest . ..... 4.5 Cross-section of the concrete floor beam to be strengthened . . . . . . . . . . . . 91 .... strengthening layer. [-] Ï. Diameter of reinforcing bars. [mm] Ï ..... Steel fibres have been used for a long time, but the modern ..... 4.0 - 5.5. 40 - 50. 100 - 150. FRC. 20 - 80. 1.5 - 5.0. 25 - 40. >500.
Graduation Thesis High Performance Fibre-Reinforced Concrete (HPFRC) for Structural Strengthening Author:
Andi Ferhati
Supervisor:
N
IV
E R S I TAT
IS
Degree in Construction Engineering Engineering Department
M
E
T
U
GO
DI
BER
UM
U
Prof. Paolo Riva
University of Bergamo
Bergamo, Italy - 2018
NS
IS
S
Dedication All the praises are to God; Special gratitude to my family.
v
Acknowledgments Words would be insufficient to adequately recognize the merit of prof. Riva, Davide Sirtoli and other people in laboratory, in the preparation of this thesis.
vii
Abstract In recent years the attention towards the restoration and strengthening of existing buildings built with reinforced concrete has gradually increased, especially because of the existence of numerous structures built according to outdated standards that consequently do not respect the requirements under current regulations. In order to increase the useful life of buildings or to make seismic adjustments, restoration of the bearing capacities or also as a result of increases in overloads, the increase of the carrying capacity of existing structures becomes fundamental, with specific reference to buildings built before the 60s of the twentieth century. The usual strengthening techniques are characterized by the use of thick reinforced concrete jackets, which cause an excessive increase in the dimensions of the buildings. It was studied the possibility of being able to moderate appreciably the thickness of this type of strengthening through the use of jackets made with High Performance Fibre-Reinforced Concrete (HPFRC). According to diagnostic investigations carried out on many buildings, it was noticed that in the past it was often used scarce quality concrete and in addition to problems related to the need for seismic improvement or adaptation, there is a need to provide a significant increase in the bearing capacity of the gravitational loads. This thesis focuses on the increase of resistance on reinforced concrete elements that have a low percentage of reinforcement or inadequate shear reinforcement, using High Performance Fibre-Reinforced Concrete jackets of reduced thickness.
ix
Contents Dedication
v
Acknowledgments
vii
Abstract
ix
General index
xv
Index of figures
xvii
Index of tables
xix
Nomenclature
xxi
1
Introduction
29
1.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
1.2
Strengthening technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
2
The material
33
2.1
The matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
2.1.1
Fibre-reinforced concrete . . . . . . . . . . . . . . . . . . . . . . . . . .
33
2.1.2
High Performance Fibre-Reinforced Concrete . . . . . . . . . . . . . . .
35
The fibres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
2.2.1
Orientation and distribution of fibres . . . . . . . . . . . . . . . . . . . .
38
2.2.2
Fibre orientation factor . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
2.3
Fibre - matrix interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
2.4
Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
2.2
xi
3
Mechanical properties
45
3.1
Mechanical properties of the composite . . . . . . . . . . . . . . . . . . . . . .
45
3.1.1
Elastic module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
3.1.2
Behaviour in compression . . . . . . . . . . . . . . . . . . . . . . . . .
45
3.1.3
Behaviour in tension . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
3.1.3.1
Direct tension tests - uniaxial . . . . . . . . . . . . . . . . . .
47
3.1.3.2
Indirect tension tests - Brazilian splitting . . . . . . . . . . . .
48
3.1.3.3
Indirect tension tests - three point bending . . . . . . . . . . .
52
3.1.3.4
Indirect tension tests - four point bending . . . . . . . . . . . .
55
3.1.3.5
Wedge Splitting Test . . . . . . . . . . . . . . . . . . . . . . .
56
3.1.3.6
Double Edge Wedge Splitting Test . . . . . . . . . . . . . . .
58
3.1.3.7
Pull-out test . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
Behaviour at high temperatures . . . . . . . . . . . . . . . . . . . . . .
58
Characterization of the adherence between HPFRC and plain concrete . . . . . .
59
3.2.1
Four point jacketed beam bending test . . . . . . . . . . . . . . . . . . .
59
3.2.2
Substrate - HPFRC adherence tests . . . . . . . . . . . . . . . . . . . . .
62
3.2.2.1
Direct tension test for the adherence . . . . . . . . . . . . . .
63
3.2.2.2
Shear test for the adherence . . . . . . . . . . . . . . . . . . .
65
Bond in tension - Simplified models . . . . . . . . . . . . . . . . . . . . . . . .
66
3.3.1
Rigid-plastic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
3.3.2
Linear elastic model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
3.3.3
Orientation effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
Bond in tension in terms of stress-strain . . . . . . . . . . . . . . . . . . . . . .
70
3.4.1
Tensile stress-strain relationship representation . . . . . . . . . . . . . .
71
3.4.1.1
Case I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
3.4.1.2
Case II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
3.4.1.3
Case III . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
3.1.4 3.2
3.3
3.4
4
Applications
77
4.1
Basic concepts regarding strengthening operations with HPFRC . . . . . . . . .
77
4.1.1
Ultimate limit state . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
4.1.2
Design strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
Application phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
4.2.1
Preparation of the support . . . . . . . . . . . . . . . . . . . . . . . . .
81
4.2.2
Positioning of metal net meshes . . . . . . . . . . . . . . . . . . . . . .
82
4.2
xii
4.3
4.2.3
Support saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
4.2.4
Jacket casting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
Applying the strengthening technique . . . . . . . . . . . . . . . . . . . . . . .
82
4.3.1
Strengthening of floors . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
4.3.1.1
The making of floor diaphragms . . . . . . . . . . . . . . . .
82
4.3.1.2
Strengthening of RC floors . . . . . . . . . . . . . . . . . . .
84
4.3.1.2.1 4.3.1.3
4.3.2
4.3.4
85
Strengthening of wooden floors . . . . . . . . . . . . . . . . .
85
4.3.1.3.1
Applicability on wooden floors . . . . . . . . . . . .
90
4.3.1.3.2
Strengthening at bending . . . . . . . . . . . . . . .
90
4.3.1.3.3
Floor strengthened with FRC hood . . . . . . . . . .
91
Beam strengthening . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
4.3.2.1
Coupling beams . . . . . . . . . . . . . . . . . . . . . . . . .
97
4.3.2.2
Applicability on beams . . . . . . . . . . . . . . . . . . . . .
98
4.3.2.3
Design strength in bending . . . . . . . . . . . . . . . . . . .
99
4.3.2.4
4.3.3
Applicability on RC floors . . . . . . . . . . . . . .
4.3.2.3.1
Rigorous method: moment-curvature diagram . . . .
99
4.3.2.3.2
Simplified method: Evaluation of the ultimate moment
99
4.3.2.3.3
Approximate method . . . . . . . . . . . . . . . . . 104
Shear design strength . . . . . . . . . . . . . . . . . . . . . . 106 4.3.2.4.1
Shear strength of the unstrengthened beam . . . . . . 107
4.3.2.4.2
Shear strength of the strengthened beam . . . . . . . 108
Column strengthening . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 4.3.3.1
Increasing capacity towards static loads . . . . . . . . . . . . . 108
4.3.3.2
Increasing capacity towards seismic loads . . . . . . . . . . . 109
4.3.3.3
Strengthening of corroded columns . . . . . . . . . . . . . . . 112
4.3.3.4
Applicability on columns . . . . . . . . . . . . . . . . . . . . 114
4.3.3.5
Design strength in compression-flexure . . . . . . . . . . . . . 115 4.3.3.5.1
M-N Domain: Rigorous method . . . . . . . . . . . 115
4.3.3.5.2
M-N Domain: Simplified method - Drawing by points 116
4.3.3.5.3
The effect of confinement . . . . . . . . . . . . . . . 119
Strengthening of nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.3.4.1
General concepts . . . . . . . . . . . . . . . . . . . . . . . . 121 4.3.4.1.1
Criticality of corner nodes . . . . . . . . . . . . . . 121
4.3.4.1.2
Internal nodes . . . . . . . . . . . . . . . . . . . . . 123
4.3.4.1.3
Corner nodes . . . . . . . . . . . . . . . . . . . . . 123 xiii
4.3.4.2
Applicability of the technique on nodes . . . . . . . . . . . . . 126
4.3.4.3
Norms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.3.4.4
Strengthening of façade nodes . . . . . . . . . . . . . . . . . . 127 4.3.4.4.1
Evaluation of the strength of unstrengthened façade nodes . . . . . . . . . . . . . . . . . . . . . . . . . 127
4.3.4.4.2 4.3.4.5
Evaluation of the strength of strengthened façade nodes 128
Strengthening of corner nodes . . . . . . . . . . . . . . . . . . 130 4.3.4.5.1
Preamble . . . . . . . . . . . . . . . . . . . . . . . 130
4.3.4.5.2
Criticality of corner nodes for calculations . . . . . . 130
4.3.4.5.3
Evaluation of the strength of unstrengthened corner nodes . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.3.5
4.3.6 5
4.3.4.5.4
Evaluation of the strength of strengthened corner nodes 135
4.3.4.5.5
Remarks . . . . . . . . . . . . . . . . . . . . . . . . 139
Strengthening of masonry . . . . . . . . . . . . . . . . . . . . . . . . . 140 4.3.5.1
Applicability of the strengthening on masonry . . . . . . . . . 144
4.3.5.2
Strengthening of walls with fibre-reinforced coatings . . . . . . 145
4.3.5.3
Shear strength . . . . . . . . . . . . . . . . . . . . . . . . . . 146
Restoration of fire damaged elements . . . . . . . . . . . . . . . . . . . 147
Conclusions
149
5.1
General conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5.2
Suggestions on future studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Glossary
151
Bibliography
155
xiv
List of Figures 1.1
FRC jacketing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
2.1
Bridging effect on fibre-reinforced concrete . . . . . . . . . . . . . . . . . . . .
34
2.2
Tensile strength classification of cementitious materials . . . . . . . . . . . . . .
35
2.3
Fibre geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
2.4
Schematic representation of different fibre composites . . . . . . . . . . . . . . .
39
2.5
Fibre orientation in 1D, 2D and 3D . . . . . . . . . . . . . . . . . . . . . . . . .
40
3.1
Behaviour of plain concrete and FRC in compression and tension . . . . . . . . .
46
3.2
Specimen geometry and instrumentation for the direct tensile test . . . . . . . . .
48
3.3
Brazilian splitting test, distribution of horizontal stresses and maximums values .
49
3.4
Typical P-COD curve of the splitting tests . . . . . . . . . . . . . . . . . . . . .
50
3.5
Strut-and-tie model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
3.6
Setup for measuring of the CMOD in a three point bending test of notched specimen 52
3.7
Machine for three point bending test on notched specimen . . . . . . . . . . . . .
53
3.8
Setup of three point bending test on notched specimen . . . . . . . . . . . . . . .
54
3.9
F-CMOD graph for FRC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
3.10 Four point bending test on notched specimen . . . . . . . . . . . . . . . . . . . .
55
3.11 Four point bending test on unnotsched specimen . . . . . . . . . . . . . . . . . .
55
3.12 Tensile and flexural behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
3.13 Wedge Splitting Test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
3.14 Plain concrete beam and HPFRC jacket geometry . . . . . . . . . . . . . . . . .
59
3.15 Load pattern on a jacketed specimen . . . . . . . . . . . . . . . . . . . . . . . .
59
3.16 Loading machine for a four point bending test of a jacketed specimen . . . . . . .
60
3.17 Load -crack split front relation for plain concrete and HPFRC jacketed specimens
61
3.18 Geometry of specimens in direct tensile bond test for adherence . . . . . . . . .
63
3.19 Set-up for direct tension test for the adherence . . . . . . . . . . . . . . . . . . .
64
xv
3.20 Geometry of specimen and set-up of the shear test for adherence . . . . . . . . .
65
3.21 Simplified stress-crack constitutive laws . . . . . . . . . . . . . . . . . . . . . .
67
3.22 Simplified model for residual strength evaluation in tension . . . . . . . . . . . .
68
3.23 Stress diagrams for residual strength evaluation in tension . . . . . . . . . . . . .
68
3.24 Typical results of bending tests with softening behaviour and linear post-cracking constitutive law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
3.25 Stress-strain constitutive laws . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
3.26 Stress-strain relations at the serviceability limit state for softening or hardening behavior of the FRC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
3.27 Stress-strain and stress-crack opening relations for uniaxial tension . . . . . . . .
73
4.1
Stress-strain models for compressed concrete . . . . . . . . . . . . . . . . . . .
78
4.2
Some seismic failure mechanisms . . . . . . . . . . . . . . . . . . . . . . . . .
83
4.3
Diagram of strengthening of floor slabs with concrete . . . . . . . . . . . . . . .
86
4.4
Typical section of an wooden floor made rigid using concrete . . . . . . . . . . .
87
4.5
Cross-section of the concrete floor beam to be strengthened . . . . . . . . . . . .
91
4.6
Cross-section of the beam strengthened with HPFRC . . . . . . . . . . . . . . .
91
4.7
Cross-section of the beam strengthened with HPFRC and polystyrene sheets . . .
92
4.8
Comparison of load-displacement curves of strengthened beams . . . . . . . . .
92
4.9
Crack pattern at failure of beam with and without reinforcement or jacket in HPFRC 93
4.10 Comparison of the load-displacement results for beams strengthened with HPFRC jacket at ULS and SLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
94
4.11 Loading frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
4.12 Strengthened section: stress and strain diagrams . . . . . . . . . . . . . . . . . . 101 4.13 Strengthened section: stress and strain diagrams (approximate method) . . . . . . 105 4.14 Cross-section of the strengthened beam . . . . . . . . . . . . . . . . . . . . . . 106 4.15 Set-up for cyclic column loading test . . . . . . . . . . . . . . . . . . . . . . . . 109 4.16 Load history and horizontal load versus displacement . . . . . . . . . . . . . . . 110 4.17 Dissipated energy during seismic test on strengthened column . . . . . . . . . . 111 4.18 Scheme for accelerated corrosion process . . . . . . . . . . . . . . . . . . . . . 112 4.19 Comparison of (column) horizontal load - displacement, drift diagram . . . . . . 113 4.20 Strengthened section of column: stress and strain distribution at ULS . . . . . . . 116 4.21 Stress and strain distribution on fully in tension column section . . . . . . . . . . 117 4.22 Stress and strain distribution on fully in compression column section . . . . . . . 118 4.23 Stress-strain relationship for confined concrete . . . . . . . . . . . . . . . . . . . 119 xvi
4.24 Results of cyclic tests for not strengthened and strengthened nodes . . . . . . . . 125 4.25 Typical beam-to-column connections . . . . . . . . . . . . . . . . . . . . . . . . 127 4.26 Strengthened column section and forces to calculate strength of the node . . . . . 129 4.27 Global collapsing mechanism for a frame structure in reinforced concrete . . . . 130 4.28 Strut-and-tie SSTM model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 4.29 Flowchart for iterative calculation of the shear strength of a node . . . . . . . . . 134 4.30 Geometry of a beam-column specimen . . . . . . . . . . . . . . . . . . . . . . . 136 4.31 Beam strengthening solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 4.32 M-N interaction diagram for a column . . . . . . . . . . . . . . . . . . . . . . . 137 4.33 Positive and negative stresses calculation diagram . . . . . . . . . . . . . . . . . 138 4.34 Forces acting on unstrengthened and strengthened node . . . . . . . . . . . . . . 139 4.35 Masonry and connector types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
xvii
xviii
List of Tables 2.1
Physical properties by type of fibre . . . . . . . . . . . . . . . . . . . . . . . . .
38
3.1
Mechanical properties of cement-based materials . . . . . . . . . . . . . . . . .
45
4.1
Strength values of materials used in design and verification formulations . . . . .
81
4.2
The substitution of the term σst · Ast . . . . . . . . . . . . . . . . . . . . . . . . 102
4.3
The substitution of the term σsc · Asc . . . . . . . . . . . . . . . . . . . . . . . 103
4.4
The substitution of the term σst · Ast with expressions . . . . . . . . . . . . . . . 104
4.5
The substitution of the term σsc · Asc with expressions . . . . . . . . . . . . . . 104
xix
xx
Nomenclature Greek letters α
Angle of inclination of the transverse reinforcement bars in relation to the beam
α
Coefficient of uncertainty on the subdivision of the soliciting shear between strut and tie
[°]
[-] αcc
Percentage of the neutral axis on which the uniform distribution of concrete compression stresses act
αF c
[%]
Percentage of the neutral axis on which the uniform distribution of the FRC compression stresses act
[%]
γm
Partial coefficient of the material
[-]
γRd
Over-resistance coefficient
[-]
ν
Reduction factor that takes into account the cracking and the reduced thickness of the strengthening layer
[-]
φ
Diameter of reinforcing bars
ρ
Geometric relationship between the area of the reinforcement bars and the area of the
[mm]
section under tension
[-]
σ2
Effective confinement tension at ULS
[MPa]
σct
Tension stress
[MPa]
σd
Average principal stress in the d direction of the diagonal strut
[MPa]
σn
Average normal tension acting on the compressed part of the section
[MPa]
θ
Inclination of concrete struts in relation to the beam axis xxi
[°]
θ
Inclination of the diagonal of the wall panel in relation to the horizontal
θ0
Inclination of concrete struts in relation to the beam axis in the case of strengthened section
[°]
[°] εd
Average strain in d direction
[‰]
εFt,I
Strain of the tensioned FRC of the caseback
[‰]
εr
Average strain in r direction
[‰]
εsc,el
Strain of the steel at the elastic limit
[‰]
εsc
Strain of the compressed reinforcement bars
[‰]
ξ
Non-dimensional coefficient
[-]
ζ
Softening coefficient
[-]
Latin uppercase letters Ag0
Area of the HPFRC jacked applied to the column
[mm2 ]
A f ST
Area of the specimen at failure
[mm2 ]
Ag
Area of the column section
[mm2 ]
As,in f Area of the lower reinforcement bars of the beam
[mm2 ]
As,i
[mm2 ]
Area of the reinforcement bars
As,sup Area of the upper reinforcement bars of the beam
[mm2 ]
Asw
Area of the transversal reinforcement
[mm2 ]
AT
Area of the unstrengthened column section
[mm2 ]
Eci
Elastic module at 28 days
[MPa]
Eci
Tangent elastic module
[MPa]
Fj
Load for CMOD = CMOD j
H
Total height of the strengthened section
[mm]
HC
Column height
[mm]
[kN]
xxii
Lbn
Net beam span
[mm]
Lb
Beam span
[mm]
Mby
Maximum resistant moment in the beam
[N · m]
Mi
Resistant moments of the beams
[N · m]
MRd
Resistant moment from equilibrium in rotation
[N · m]
N
Axial force acting on the column
[kN]
NE d
Vertical axial compression on the masonry wall panel
[kN]
PST
Compression force
[kN]
Vc
Shear force on the column
[kN]
Vn
Total shear force acting on the node
[kN]
VRd,m Shear resistance of the masonry
[kN]
VRd,r
Shear resistance of the FRM coating
[kN]
VRdc
Shear resistance of the core concrete
[kN]
VRds
Shear resistance of the transverse reinforcement
[kN]
VRd
Design shear strength of strengthened masonry
[kN]
VSd
Shear force acting on the upper part of the node
[kN]
Latin lowercase letters ac
Height of the compressed part of the section of the column
[mm]
b
Specimen width
[mm]
bj
Effective width of the node
[mm]
br
Strut/tie width
[mm]
bw
Section width
[mm]
c
Concrete cover
[mm]
d
Useful height of the section
[mm] xxiii
df
Diameter of the fibres
0 fcd
Compressive strength of the core concrete
[MPa]
fc0
Cylindrical compressive strength of concrete
[MPa]
fR 3
Equivalent post-crack strength for the ULS
[MPa]
fa
Average compression stress acting on the column section
[MPa]
fcd
Cylindrical design compressive strength of the FRM mortar
[MPa]
fcd
Design compressive strength of concrete
[MPa]
fck
Characteristic compressive strength
[MPa]
fctm
Tensile strength
[MPa]
fF cm
Nominal value of the compressive strength
[MPa]
[µm]
fFt,max Maximum tensile strength
[MPa]
fFt d
[MPa]
Design tensile strength of the HPFRC
fFtu,d Ultimate tensile strength of FRM mortar
[MPa]
fR, j
Tensile strength for residual bending
[MPa]
fR1
Equivalent post-crack strength for SLS
[MPa]
fvd
Design shear strength of the masonry
[MPa]
fyd,c
Design yield strength of the compressed reinforcement bars
[MPa]
fyd,t
Design yield strength of tensed reinforcement bars
[MPa]
fyd
Design yield stress of the reinforcement
[MPa]
h
Height of the masonry wall panel
[mm]
h
Section height
[mm]
hb
Height of the beam
[mm]
hc
Width of the column
[mm]
hj
Distance between the most external bars of the column reinforcement
[mm]
xxiv
hsp
Distance between the point where the notch ends and the top surface of the specimen [mm]
l
Distance between supports
[mm]
l
Width of the masonry wall panel
[mm]
l0
Length of the compressed part of the masonry wall
[mm]
lf
Length of the fibres
[mm]
s
Step of the transverse reinforcement
[mm]
sL
Lateral thickness of the strengthening layer
[mm]
sr m
Average value of the distance between the cracks
[mm]
tm
Wall thickness
[mm]
tr
Total coating thickness
[mm]
wu
Maximum crack opening accepted in the structural project
[µm]
y
Neutral axis distance from the tensed edge of the section
[mm]
zb
Arm of the internal couple
[mm]
xxv
xxvi
Preface The writing of this thesis, supervised by Prof. Riva, was carried out during year 2018 with some experimental tests performed in the laboratory of material testings of the University of Bergamo. I hope this thesis will be read and examined critically and that comments and suggestions regarding its contents are addressed to me. Andi Ferhati
Background image on the front cover and image of the back cover [12] Background image on Abstract and on the beginning page of every chapter [12] Reviewed version 1.1, published on 2018-07-07.
xxvii
xxviii
Chapter 1
Introduction 1.1
Overview
Recent earthquakes around the world have shown the vulnerability of reinforced concrete beamcolumn joints in relation to seismic loads. The joints have been identified as critical structural elements, which are prematurely failing and therefore have been defined as weak connections in the RC frame constructions. A typical failure in poorly designed joints with unsuitable transverse reinforcement is under shear in the form of diagonal tension. This was also noticed in missing stirrup around reinforcement bars, especially in the internal joints where the bars are not anchored correctly with standard hooks.[1]
1.2
Strengthening technique
The structural strengthening of reinforced concrete structural elements is done with a variety of techniques. The most common is the jacketing with reinforced concrete or with steel.[2] It requires intensive work, skills in the realization of details and results in an increase in the dimensions and weight of the structural elements.[3] [1]
Thomas Paulay and Michael John Nigel Priestley. Seismic Design of Reinforced Concrete and Masonry Buildings.
Aug. 2009. 768 pp. isbn: 978-0-471-54915-4. doi: 10.1002/9780470172841. [2] Sergio Alcocer and James O. Jirsa. “Strength of reinforced concrete frame connections rehabilitated by jacketing”. In: ACI Structural Journal 90 (May 1993), pp. 249–261. [3] Costas P. Antonopoulos and Thanasis C. Triantafillou. “Experimental Investigation of FRP-Strengthened RC BeamColumn Joints”. In: Journal of Composites for Construction 7.1 (2003), pp. 39–49. doi: 10.1061/(ASCE)10900268(2003)7:1(39).
29
Index > 1 Introduction > 1.2 Strengthening technique Another type of strengthening involves the use of FRP composites or Carbon-FRP (C-FRP)[4] for the making of the jacket on elements to be strengthened. Among the most important advantages that this technique offers, is the rapidity of the intervention, the immediate adaptability of the strengthening layer to the structures, less weight than the traditional materials, more strength. Therefore it can be said that this type of strengthening is a sound alternative to the traditional techniques of seismic improvement and adaptation and to the strengthening of structural elements of various kinds. Among the most important disadvantages is the inability to guarantee a sufficient margin of safety in relation to high operating temperatures, making many interventions problematic.
FRC jacket
Pier bar
FRC jacket
Footing anchorage bar
Figure 1.1: FRC jacketing[7] The technique of retrofitting using externally tied steel plates instead, gained popularity because of being rapid, causing minimal disturbances in the place of intervention and affecting minimally the size of the sections. However, several problems have been encountered with this technique, including undesired shear failure, difficulty in handling heavy steel plates and corrosion.[5][6] An alternative solution that allows to considerably reduce the thickness of the strengthening layer, considers the adoption of jackets in High Performance Fibre-Reinforced Concrete (HPFRC). [4]
Chris G. Karayannis and George M. Sirkelis. “Strengthening and rehabilitation of RC beam–column joints using
carbon-FRP jacketing and epoxy resin injection”. In: Earthquake Engineering & Structural Dynamics 37.5 (Feb. 2008), pp. 769–790. doi: 10.1002/eqe.785. url: https://onlinelibrary.wiley.com/doi/abs/10.1002/eqe.785. [5] R Jones, R N. Swamy, and Abdelhamid Charif. “Plate separation and anchorage of reinforced concrete beams strengthened by epoxy-bonded steel plate”. In: Structural Engineer 66 (Mar. 1988). issn: 1466-5123. [6] Y.N. Ziraba, M Baluch, I.A. Basunbul, Alfarabi Sharif, A.K. Azad, and G.J. Al-Sulaimani. “Guidelines toward the design of reinforced concrete beams with external plates”. In: ACI Structural Journal 91 (Nov. 1994), pp. 639–646. doi: 10.14359/1538.
30
Index > 1 Introduction > 1.2 Strengthening technique This technique, by adopting a material more similar to the plain concrete than any other solution, solves the problem of compatibility between different materials. In addition, it is efficient for strengthening towards static loads, in particular for the increase of the flexural and shear capacity of RC beams[7] and For the static and seismic strengthening of columns, beam-column internal nodes and coupling beams, especially in cases where the element is built with low strength concretes. This effect is not often achieved with other solutions such as Beton-plaque or FRP applications.[8] The purpose of this thesis is to bring a general overview of the strengthening technique with HPFRC material, elaborating on the applicative aspects the strengthening of various structural elements such as floor slabs, beams, columns, nodes and masonry. In the following chapters will be seen in detail HPFRC as a material, its mechanical characteristics and will be studied in deep the technique application particularities for the different structural elements.
[7]
Bruno Massicotte and Guillaume Boucher-Proulx. “Seismic Retrofitting of Rectangular Bridge Piers With
UHPFRC Jackets”. In: Designing and Building with UHPFRC: State of the Art and Development. Ed. by François Toutlemonde and Jacques Resplendino. Wiley-ISTE, Jan. 2008. isbn: 9781848212718. doi: https://doi.org/10. 1002/9781118557839.ch35. [8] G. Martinola, A. Meda, G.A. Plizzari, and Z. Rinaldi. “An application of high performance fiber reinforced cementitious composites for RC beam strengthening”. In: FRAMCOS 6 (June 2007).
31
Index > 1 Introduction > 1.2 Strengthening technique
32
Chapter 2
The material 2.1
The matrix
In this chapter will be brought, in relation to the indications provided by fib Model Code for Concrete Structures 2010,[9] where necessary integrated with the information contained in CNR-DT 204/2006 - Istruzioni per la Progettazione, l’Esecuzione ed il Controllo di Strutture di Calcestruzzo Fibrorinforzato,[10] the description of the main characteristics of the material and the possible schematizations of the constituent bonds to be adopted during the design of strengthening interventions with fibre-reinforced concrete.
2.1.1
Fibre-reinforced concrete
The fibre-reinforced concrete originates from the 19th century, the first patent is American in 1874. Modern research on fibre-reinforced concrete began in The United States in the mid-1950s. In the years 70 of the twentieth century, the commercial use of this material began to increase, especially in Europe, Japan and USA.[11] The common areas of application today are paving, industrial floors, prefabricated elements and various types of repairs, renovations. Generally, concrete containing a hydraulic cement, water, fine and coarse aggregate and discrete discontinuous fibres is called Fibre-Reinforced Concrete (FRC). It is possible to use fibres of [9]
International Federation for Structural Concrete (fib). fib Model Code for Concrete Structures 2010. Ernst &
Sohn, Oct. 2013. 436 pp. isbn: 978-3-433-03061-5. doi: 10.1002/9783433604090. [10] CNR-DT 204/2006 - Istruzioni per la Progettazione, l’Esecuzione ed il Controllo di Strutture di Calcestruzzo Fibrorinforzato. Italian. Consiglio Nazionale delle Ricerche. CNR, July 2006. [11] R Vollum, J Clarke, and N Swannell. Technical Report 63 - Guidance for the design of steel-fibre reinforced concrete. Tech. rep. 2007.
33
Index > 2 The material > 2.1 The matrix various shapes and sizes made of steel, synthetic materials, glass and natural materials. However, for most structural and non-structural purposes, steel fibres (Figure 2.1[12] ) are the most used of all fibrous materials, while synthetic fibres (e.g. of polypropylene and nylon) are mainly used to control plastic micro-cracks in slabs.
w
Figure 2.1: Bridging effect on fibre-reinforced concrete[12]
Compared to conventional strengthening, the characteristics of the strengthening technique with fibre-reinforced concrete are: 1. The fibres are generally distributed in the section, while the reinforcing bars are placed only where necessary; 2. The fibres are relatively short and close between them, while the reinforcing bars are continuous and not closely positioned; 3. It is generally not possible to make the same reinforcing surface with fibre-reinforced concrete as with the reinforcing bars. This means that, unlike the ordinary reinforced concrete, with adequate minimum reinforcement with FRC, a softening behaviour is observed after cracking (see Figure 2.2[13] ). Differently from the normal concrete, strength is increased significantly as a result of the fibres transmitting the force through the cracks. [12]
Ingemar Löfgren. “Fibre-reinforced Concrete for Industrial Construction - a fracture mechanics approach to
material testing and structural analysis”. PhD thesis. Chalmers University of Technology, Dec. 2005, [13] Alessandro P. Fantilli, Hirozo Mihashi, and Paolo Vallini. “Crack profile in RC, R/FRCC and R/HPFRCC members in tension”. In: Materials and Structures 40.10 (Jan. 2007). issn: 1871-6873. doi: 10.1617/s11527-006-9208-7, p. 13.
34
Index > 2 The material > 2.1 The matrix The main advantage of including fibres in matrices is the improvement of the ductility and the post-peak stress-strain/cracking relationship. The types of fibres commonly used are of steel, glass, carbon, polyvinylic alcohol (PVA), polypropylene (PP) and of cellulose. 4
σct [MPa]
4
Strain hardening HPFRC
3
3
2
2
1
1
0
Strain softening Plain Concrete 0 0 0.75 1.5 w [mm]
0
0.4
0.8 εc [%]
1.2
1.6
Strain softening FRC
2.25
3
Figure 2.2: Tensile strength classification of cementitious materials[13] The constituents of a composite are generally arranged so that one or more discontinuous phases are incorporated into a continuous phase. The discontinuous phase is defined the reinforcement and the continuous phase is the matrix. In all composite materials, the fibres are added to improve the properties and behaviour of the material and these fibres can be continuous or discontinuous (i.e. short), with a preferred orientation (e.g. uni-directional or bidirectional) or random. The main factors influencing the performance of a composite material are: 1. The physical properties of the fibres and matrix; 2. The strength and bond between the fibres and the table; 3. The amount of fibres (volume fraction) and their distribution and orientation.
2.1.2
High Performance Fibre-Reinforced Concrete
Part of the typology of fibre-reinforced concretes are also cementitious compositions denominated High Performance Fibre-Reinforced Concrete (HPFRC) which are characterized by higher strength. FRC concretes are characterized or defined as "high performance", HPFRC, if the stress-strain curve shows quasi-hardening or pseudo-hardening behavior. Generally HPFRC materials exhibiting hardening show a diffuse cracking framework. 35
Index > 2 The material > 2.2 The fibres The UHPFRC concrete - Ultra High Performance Fibre-Reinforced Concrete) has a compression strength higher than 150 MPa (or according to other sources: higher than 200 MPa).
2.2
The fibres
There are a wide range of fibres that can be used to improve strength and other properties of concrete and cementitious composites. Steel fibres have been used for a long time, but the modern steel fibres have more slenderness, more complex geometries and are often made with high strength steel. In addition, synthetic fibres are becoming particularly appealing since the possibility to provide an effective strengthening comparable to that of steel fibres. The types of synthetic fibres that have been used in cement matrices include: polyethylene (PE), polypropylene (PP), acrylic (PAN), polyvinyl acetate (PVA), polyamides (PA), Aramid, polyester (PES) and carbon.[14] These parameters are considered important: 1. The length and diameter of the fibres; 2. The equivalent diameter, in other words the diameter of the circle equivalent to the fibre section considered see Figure 2.3(a); 3. The aspect ratio, defined as the ratio of the length to the diameter of the fibre. It influences the transfer of the efforts between the cement matrix and the fibre itself; It is also one of the factors responsible for the workability of the mixture in fresh state; 4. The volumetric percentage in relation to the total. This influences the relative distance between the fibres within the composite and thus the diffusion of stress which, in macroscopic level, brings to the identification of the failure behaviour; 5. The shape (smooth, wavy, hooked, etc., see Figure 2.3(b)). So that fibres can be effective in their function inside cementitious matrices, it has been found (by experiments and analytical studies) that they should have the following properties: 1. A tensile strength significantly higher than the matrix (two to three orders of magnitude); [14]
Arnon Bentur and Sidney Mindess. Fibre Reinforced Cementitious Composites. Second Edition. Modern
Concrete Technology. Taylor & Francis, 2006. 624 pp.
36
Index > 2 The material > 2.2 The fibres 2. An adherence/bonding with the cement matrix, preferably of the same degree or higher than the tensile strength of the matrix; 3. An elastic modulus in tension significantly higher than that of the matrix (at least 3 times); 4. Ductile enough so that the fibre does not break due to abrasion or bending of the fibre; 5. The coefficient of Poisson and the coefficient of thermal expansion should preferably be of the same order for both the fibre and the matrix; 6. It is important that the fibres be durable and able to withstand highly alkaline environment.
Circular
Quadratic
Rectangular
Triangular
Elliptical
Hexagon
Octagon
Irregular
Straight
End-hooks
Paddles
crimped Bow shaped Toothed (wave shaped)
End knobs
Coned
Surface indented
Irregular
Twisted
(a) Cross-sectional geometries of fibres (b) Typical fibre shapes
Figure 2.3: Fibre geometries[12]
The tensile strength of the fibre can be increased if necessary to avoid the fracture of the fibre. The commonly used steel fibres have a round section, a diameter ranging from 0.2 to 1 mm, a length ranging from 10 to 60 mm, and a dimensional ratio of less than 100 (typically ranging from 40 to 80). The fibres often show a sort of deformation or anchorage shape to increase their performance. The synthetic fibres can have a small diameter of 10 µm, for example the Kevlar, carbon or glass, and large diameter of 0.8 mm for polypropylene and PVA fibres. In general, the cross-section of a single fibre can be circular, rectangular, diamond, squared, triangular, flat, polygonal or of any substantially polygonal shape. To improve the characteristics of adherence, a fibre can be modified along its length by making its surface rougher or including mechanical deformations. As a result, the fibres can be smooth, serrated, warped, folded, rolled, twisted, with terminal hooks, shovels, buttons, or other types of anchors. 37
Index > 2 The material > 2.2 The fibres
Material
Specific
Tensile
Elastic
Ultimate
weight
strength
modulus
stretching
[g/cm3 ]
[MPa]
[GPa]
[%]
5-1000
7.85
200-2600
195-210
0.5-5
Glass E
8-15
2.54
2000-4000
72
3.0-4.8
Glass AR
8-20
2.70
1500-3700
80
2.5-3.6
Acrylic (PAN)
5-17
1.18
200-1000
14.6-19.6
7.5-50.0
Aramid (e.g. Kevlar)
10-12
1.4-1.5
2000-3500
62-130
2.0-4.6
Carbon (low modulus)
7-18
1.6-1.7
800-1100
38-43
2.1-2-5
Carbon (high modulus)
7-18
1.7-1.9
1500-4000
200-800
1.3-1.8
Nylon (Polyamide)
20-25
1.16
965
5.17
20.0
Polyester (e.g. PET)
10-8
1.34-1.39
280-1200
10-18
10-50
25-1000
0.96
80-600
5.0
12-100
Polypropylene (HPPE)
-
0.97
4100-3000
80-150
2.9-4.1
Polyvinyl acetate (PVA)
10-200
0.90-0.91
310-760
3.5-4.9
6-15.0
3-8
1.2-2.5
800-3600
20-80
4-12
Type of fibre
Diameter [µm]
Metallic
Steel
Glass
Synthetic
Polyethylene (PE)
Cellulose (Wood) Natural
Coconut
100-400
1.12-1.15
120-200
19-25
10-25
organic
Bamboo
50-400
1.50
350-50
33-40
-
Hessian
100-200
1.02-1.04
250-350
25-32
1.5-1.9
Natural
Asbestos
0.02-25
2.55
200-1800
164
2-3
inorganic
Wollstonite
25-40
2.87-3.09
2700-4100
303-530
-
Table 2.1: Physical properties by type of fibre[12] Some fibre properties of different materials are shown in Table 2.1.[12]
2.2.1
Orientation and distribution of fibres
The orientation of the fibre plays an important role for the mechanical performance of the fibre-reinforced composites. Dispersed strengthening technology provides directional and random (free) orientation of the fibres in the concrete body. Directional orientation, see Figure 2.4 (a)-(e), is done mainly using continuous filaments, braids, various types of fabrics and non-fabric nets, or from particular production techniques such as pre-introduction of the fibres or for example with the glsHatcheck process. The random orientation is characterized by equally probable and free distri38
Index > 2 The material > 2.2 The fibres bution of short fibres throughout the body of the concrete, in three-dimensional space. Figure 2.4(f)
The inclination angles of the fibres relative to the surface of the cast element vary from zero to 90°, provided that the size of the element, considerably exceeds the length of the fibres in all directions. The random-in-plane orientation is characterized by the free and unlimited distribution of fibres in a two-dimensional space. The smaller the cross section, the more limited is the possibility of free orientation of the fibres. However, it should also be noted that for fibrereinforced concrete There are a number of other factors affecting the orientation of the fibre and distribution in addition to purely geometrical considerations - such as the method of placement, the equipment used and the properties of the fresh concrete (resistance against segregation of the fibres).
(a)
(e)
(c)
(b)
(g)
(f)
(d)
(h)
Figure 2.4: Schematic representation of different fibre composites: (a) continuous uni-directional; (b) continuous bi-directional; (c) discontinuous with polarized 1D fibre orientation; (d) discontinuous with polarized 2D fibre orientation; (e) discontinuous with random-in-plane orientation; (f) discontinuous with random fibre orientation; (g) composite particles (suspensions of particles); (h) fibre-reinforced composite and particles[12]
To determine the mechanical behaviour of the different composites presented in Figure 2.4 is necessary to consider the orientation of the fibres. For this purpose it is common to define the efficiency factor of the fibre, ηb , as the efficiency of bridging, in other words, the amount of fibres to sew a crack. In the case of a one-dimensional (1D) system it is quite simple to determine the efficiency of the fibre, which is optimal since all the fibres are oriented in the direction of the load. For this case the efficiency of the fibre is equal to one (ηb.1D = 1), while the embedding length varies from half the length of the fibre to zero (0 < Le ≤ L f /2); In Figure 2.5(a) a schematic 39
Index > 2 The material > 2.2 The fibres presentation from Stang and Li, 2001[15] of the fibre orientation in one dimension.
2.2.2
Fibre orientation factor
In line with what has been said in fib Model Code for Concrete Structures 2010, the mechanical effects associated with the orientation of the fibres can be measured with the identification of an orientation coefficient K. The experimental investigations have demonstrated that the behaviour evaluated by standard direct and indirect tensile tests can be considerably change, both in positive and negative terms, compared to the mechanical reaction of the same material when applied to real structures. Making structural specimens, able to faithfully reproduce the application conditions, allows to estimate the values of K different from the isotropic situation (K = 1). In particular, are identified favourable conditions (K < 1) and unfavourable conditions (K > 1) influencing the constitutive laws of design nature.
y
y
crack plane
crack plane
Lf
x
φ
x
Le z
Le
z Lf
(a) Fibre orientation in 1D
(b) Fibre orientation in 2D z
r′
f
φ2 y
φ1
x
(c) Fibre orientation in 3D
Figure 2.5: Fibre orientation in 1D, 2D and 3D[12] [15]
Henrik Stang and Victor Li. Mechanics of Fibre Reinforced Cement based Composites. Lyngby, Denmark, 2001.
40
Index > 2 The material > 2.3 Fibre - matrix interface The constitutive laws obtained from notched specimens and structural specimens with favourable orientation of the fibres may differ substantially. In overall terms, the effects related to the orientation of the fibres can be prudently neglected, provided that HPFRC is not used for structural elements of well defined bi-axial behaviour, for example the slabs from bridge solicited by substantial transverse bending actions. In presence of significant anisotropic behaviour, it may be advantageous to introduce nets in the thin layers of HPFRC, specifically in glass alkali-resistant (AR), in order to stabilize the cracking process and ensure a strong hardening behaviour in bending and uniaxial tension.
2.3
Fibre - matrix interface
The microstructure of the matrix near the strengthening fibres has a particular composition compared to other areas of the cementitious conglomerate. This specific area takes the name of the interface transition zone, also called ITZ;[16] Its nature and its extent depend strongly on the type of fibres present and the production process used. Two cases will be distinguished in the description of the behaviour of this zone. In the first case, that of mono-filament fibres, the fibres are isolated from each other; Therefore the entire surface of the fibre is in contact with the cementitious matrix. In the case of fibres in bundles only the outer part of the bunch of fibres has a direct contact with the cement paste. For the case of mono-filament fibres experimental studies have shown that ITZ is rich in calcium hydroxide (C-H) and much more porous than the rest of the matrix. The porous nature of the transition zone is the result of the interaction between calcium silicate hydrate (C-S-H) and ettringite. The result of the C-H rich area around the fibre surface is due to its precipitation from the solution in the space around the fibre. Water particles are attracted to the surface by the fibres within the mixture and create a high porosity layer in the interface area. After maturation, the water consumed by the chemical process leaves some voids that favour the concentration of the crystals of portlandite.[17]
[16]
Piet Stroeven, Huisu Chen, Jing Hu, and Jianjun Zheng. “Interfacial Transition Zone (ITZ) in plain and fiber
concrete”. In: Proceedings of the 6th International RILEM Symposium on Fibre Reinforced Concretes. RILEM Publications SARL, 2004, pp. 903–912. isbn: 2-912143-51-9. [17] Arnon Bentur, Sidney Diamond, and Sidney Mindess. “Cracking processes in steel fiber reinforced cement paste”. In: Cement and Concrete Research 15.2 (1985), pp. 331–342. issn: 0008-8846. doi: https : / / doi . org/10.1016/0008- 8846(85)90045- 6. url: http://www.sciencedirect.com/science/article/pii/ 0008884685900456.
41
Index > 2 The material > 2.4 Fibre - matrix interface In the case of a cementitious matrix with a very well-designed composition, with fine fillers and inerts with a contained diameter, and with fibres of very small cross-section, the previously described transition zone can be safely eliminated. In this perspective, the cross section of the fibrous strengthening layer becomes a property to be taken into consideration for a good design mix in order to obtain a matrix with sufficiently dense microstructure. Regarding the bundle fibres, if not separated during the production process, the fibres will remain grouped in bundles. The resulting microstructure is characterized of empty spaces between the filaments, gaps where the cement paste is not able to penetrate, or by localized areas of non-uniform deposition of hydration products. The fibres will therefore have relative freedom to move in relation to each other. The weakest component of the fibre-matrix bond is not the direct contact between the two materials, but the immediately next layer rich in crystals. This is the area responsible for the strength of the material and the tensile failure takes place with the simultaneous formation of cracks both at the interface and in the matrix, which then unite and propagate in an unstable manner until collapse happens. The main types of interaction that prevent the cracking phase in this area are these: 1. Chemical and physical adhesion; 2. Friction; 3. Mechanical anchorage induced by the deformation of the fibres. The chemical adhesion is improved by introducing high percentages of flying ash or silica smoke, as mentioned above, reducing the crystallization of C-H and thinning the ITZ[18] .[19] In some cases, however, even a good dosage of the mixture’s design is not sufficient to guarantee adequate strength. For the other two aspects it is necessary to treat the subject in relation to the fracture mechanics of the material. It is here anticipated that the characteristic strength can be increased also by adding mechanical bonders, thus increasing the surface roughness of the fibres or by shaping special anchorages.
[18]
Yin-Wen Chan and Victor C. Li. “Effects of transition zone densification on fiber/cement paste bond strength
improvement”. In: Advanced Cement Based Materials 5.1 (1997), pp. 8–17. issn: 1065-7355. doi: https : //doi.org/10.1016/S1065-7355(97)90010-9. url: http://www.sciencedirect.com/science/article/ pii/S1065735597900109. [19] Xiao Hui Wang, Stefan Jacobsen, Siaw Foon Lee, Jian Ying He, and Zhi Liang Zhang. “Effect of silica fume, steel fiber and ITZ on the strength and fracture behavior of mortar”. In: Materials and structures 43.1-2 (2010), p. 125.
42
Index > 2 The material > 2.4 Classification
2.4
Classification
The classification of the fibre-reinforced concrete is based on the post-cracking residual tensile strength. The particular curves of a fibre-reinforced composition all have an upward line until the first cracking, regardless of the type of reinforcement used. It will be the progression of the line from that point on to determine the different behaviour of the composite material. It is assumed a linear elastic behaviour considering the characteristic values of the residual flexural strength in serviceability conditions ( fR1k ) and at ultimate limit state ( fR3k ). Each FRC is classified according to two parameters: • fR1k that represents the strength range; • A character a, b, c, d or e that represents the ratio between fR3k and fR1k . The strength range is defined by two consecutive numbers in the series: 1; 1.5; 2; 2.5; 3; 4; 5; 6; 7; 8 [MPa] while the characters a, b, c, d, e correspond to the following ratios of the residual strengths: a for 0.5 ≤ b for 0.7 ≤ c for 0.9 ≤ d for 1.1 ≤ e for 1.3 ≤
fR3k fR1k fR3k fR1k fR3k fR1k fR3k fR1k fR3k fR1k
≤ 0.7 ≤ 0.9 ≤ 1.1 ≤ 1.3
For example, a material named "3b" is characterized by a strength fR1k between 3 and 4 MPa and a ratio fR3k / fR1k between 0.7 and 0.9. The designer must also specify the material of the fibres.
43
Index > 2 The material > 2.4 Classification
44
Chapter 3
Mechanical properties 3.1
Mechanical properties of the composite
In Table 3.1[20] are listed some mechanical properties of cement-based materials. fc [MPa]
ft [MPa]
E [GPa]
G f [Nm/m2 ]
Cement paste
10 - 25
2.0 - 10.0
10 - 30
≈10
Mortar
5 - 10
1.0 - 10.0
10 - 30
10 - 50
Plain concrete
20 - 80
1.5 - 5.0
25 - 40
50 - 150
HSC
>80
4.0 - 5.5
40 - 50
100 - 150
FRC
20 - 80
1.5 - 5.0
25 - 40
>500
>80
5.0 - 10.0
30 - 50
>1000
Material
HPFRC
Table 3.1: Mechanical properties of cement-based materials[20]
3.1.1
Elastic module
The value of the modulus of elasticity of the FRC is generally not very influenced by the fibres.
3.1.2
Behaviour in compression
The fibres, although being often able to lower the fragility of the concrete, do not affect much the compression behavior. The constitutive bond of FRC and its strength can be compared to those of unstrengthened material up to peak load. The effect of the fibres appears after reaching the [20]
Serena Mostosi, Paolo Riva, and Giovanni Plizzari. “Strengthening of RC beams with high performance concrete”.
PhD thesis. Università degli Studi di Brescia, Jan. 2012.
45
Index > 3 Mechanical properties > 3.1 Mechanical properties of the composite maximum load, with the lowering of the fragility of the material, especially when using HPC, as shown in Figure 3.1. For a normal strength concrete, the aggregate is significantly more resistant than the products of cement hydration. For a high performance concrete, however, the resistance of the aggregates contained in it, when compared with the resistance of the matured mortar changes very little. Consequently, in High Performance Concretes, some cracks extend through the aggregates producing cracking frameworks of softer tortuosity than those of normal strength concretes. In HPC, the tensile strength of the aggregate, rather than the interface between paste and aggregates, can become the weak bond.[21] σ = σ (w)
Multiple cracking
120
Plain concrete (HSC)
100
Stress [MPa]
σ = σ (ε)
Crack localization
FRC
σ
σ = σ (w)
σw
Increase of Vf
80
σ (ε) σt
Crack localization Strain softening: Fibre-reinforced concrete
60 40
Strain softening: Plain concrete
Plain concrete (NSC) FRC
20
Strain hardening: High-performance Fibre-reinforced Concrete
E
deformation
0 0
1
2
3
4
5
6
7
8
ε
Strain [10-3]
ε
(a)
w w
(b)
Figure 3.1: Behaviour of plain concrete and FRC in (a) compression and (b) tension[12]
3.1.3
Behaviour in tension
The behaviour in tension is mainly influenced by the presence of fibres. Unlike the fragile behaviour noted in plain concrete, in FRC composites the stress-strain curve is not limited to the elastic branch line but continues in a softening or hardening behaviour according to the percentage of fibre and their orientation. Naaman and Reinhardt identifies the point of division between glssoftening and glshardening behaviour in the 2% volumetric fibre percentage. As shown in Figure 3.1(b) an increase in the percentage of fibres results in increased energy dissipation and [21]
David Darwin, S Barham, R Kozul, and S G. Luan. “Fracture energy of high-strength concrete”. In: ACI
Materials Journal 98 (Sept. 2001), pp. 410–417.
46
Index > 3 Mechanical properties > 3.1 Mechanical properties of the composite multi-cracking with more stable failure.[22]
For the determination of the tensile strength in proposed a performance approach in order to identify experimentally the constitutive curve through appropriate tests. The nominal tension-crack opening relation can be determined by uniaxial tensile tests or bending tests. In this regard, it is important to underline how the peak resistances exhibited by FRC composites are deeply dependent on the orientation of the fibres distributed within the cementitious matrix.[23]
3.1.3.1
Direct tension tests - uniaxial
The characteristics of the specimens and the specifications relating to the test set-up complying with UNI U73041440 - Progettazione, esecuzione e controllo degli elementi strutturali in calcestruzzo rinforzato con fibre d’acciaio[24] are those described in CNR-DT 204/2006 - Istruzioni per la Progettazione, l’Esecuzione ed il Controllo di Strutture di Calcestruzzo Fibrorinforzato. The test aims to identify the stress-strain curve, of the first and last cracking resistance and the corresponding deformations. The specimen has dimensions and geometry shown in Figure 3.2 (on the left) according to CNR-DT 204/2006 - Istruzioni per la Progettazione, l’Esecuzione ed il Controllo di Strutture di Calcestruzzo Fibrorinforzato. The total length is 330 mm. The thickness, t p , of the specimen should be larger than 5 times the maximum diameter of the aggregate and however not smaller than 13 mm. The width, b p , should be larger than 5 times the maximum diameter of the aggregate and in any case no smaller than 30 mm. The samples can be obtained by cutting the structural element or cast simultaneously in separate forms with the same practices and the same disposition of the structural element. If cast in a separate form, the specimen must be matured in the same way as the structural element. The test machine must comply with the norm EN 12390-4 - Testing hardened concrete - Part 4: [22]
A.E. Naaman and H.W. Reinhardt. “PRO 30: 4th International RILEM Workshop on High Performance Fiber
Reinforced Cement Composites (HPFRCC 4)”. In: RILEM Publications v. 1 (2003). url: https://books.google. it/books?id=p5IMbceJOSsC. [23] Liberato Ferrara, Nilufer Ozyurt Zihnioğlu, and Marco Di Prisco. “High mechanical performance of fibre reinforced cementitious composites: The role of "casting-flow induced" fibre orientation”. In: Materials and Structures 44 (Jan. 2011), pp. 109–128. doi: 10.1617/s11527-010-9613-9. [24] UNI U73041440 - Progettazione, esecuzione e controllo degli elementi strutturali in calcestruzzo rinforzato con fibre d’acciaio. Italian. Ente Nazionale Italiano di Unificazione. UNI, 2004.
47
Index > 3 Mechanical properties > 3.1 Mechanical properties of the composite Compressive strength - Specification for testing machines[25] and must be equipped with a suitable device which allows to carry out the tests with displacement control. The control parameter must be increased at a constant speed of 0.05 ± 0.01 mm/min. Both the load and the displacement must be continuously recorded. The apparatus measures the relative displacement between two points far 80 mm in at least 2 opposite positions, as shown in Figure 3.2 (on the right).
P 85
2 bp
tp
40
80
bp
80
40
85
P Figure 3.2: Specimen geometry and instrumentation for the direct tensile test[10] The specimen is seized by appropriate clamps at the two ends, adopting possible measures to diffuse the local pressure. The clamps must be free to rotate in all directions, for example by using spherical joints. The fastening of the specimen to the clamps can be carried out by friction or by gluing with epoxy adhesive. Direct tensile tests of dog-bone shaped specimens were carried out in the laboratory of material testings of the University of Bergamo with the collaboration of Davide Sirtoli and with the technical assistance of Daniele di Marco.
3.1.3.2
Indirect tension tests - Brazilian splitting
The practical difficulties of carrying out the direct tension test have led to alternative procedures, such as the indirect tension test by splitting, also called the brazilian test. It is denominated as [25]
EN 12390-4 - Testing hardened concrete - Part 4: Compressive strength - Specification for testing machines.
European Committee For Standardization. Rue de Stassart, 36 - B-1050 Brussels, 2000.
48
Index > 3 Mechanical properties > 3.1 Mechanical properties of the composite indirect because using the geometry of the specimen a compression force is applied to obtain the tensile strength characteristics of the material.
Compression
Tension
(a)
(b)
(c)
Figure 3.3: (a) Brazilian splitting test; (b) distribution of horizontal stresses; (c) Maximums values[27]
The test (Figure 3.3) consists in submitting a cylindrical specimen (cubic or prismatic tests can also be used) to a compression force applied to a limited zone for the entire length of the cylinder.[26] The failure takes place when is reached the maximum tensile strength in the direction orthogonal to the direction of application of the compression stress. From the maximum load the indirect tensile strength of the material is obtained. To determine this property, it is referred to ASTM C496 / C496M-17 - Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens[27] and to EN 12390-4 - Testing hardened concrete - Part 4: Compressive strength - Specification for testing machines. For ordinary concrete, it is possible to deduce the direct tensile strength from the indirect (EN 1992-1-1 Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings[28] ). Similar correlations for fibre-reinforced [26]
Lorenzo Elli, Liberato Ferrara, and Marco G. L. Lamperti Tornaghi. “Identificazione sperimentale del comporta-
mento a trazione di calcestruzzi fibrorinforzati: confronto fra metodi di misura tradizionali e digital image correlation”. Italian. MA thesis. Politecnico di Milano, 2013. [27] ASTM C496 / C496M-17 - Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens. ASTM International. West Conshohocken, PA, USA, 2017. doi: 10.1520/C0496_C0496M-17. [28] European Committee for Standardization. EN 1992-1-1 Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings. European Committee For Standardization. Rue de Stassart, 36 - B-1050 Brussels: CEN, 2005.
49
Index > 3 Mechanical properties > 3.1 Mechanical properties of the composite concrete are not currently codified. Generally this type of test is used for the research of the characteristics of first cracking and ends with a sudden and violent failure of the specimen. As a test therefore, it is inappropriate for the analysis of the material behaviour in the post-cracking phase, a crucial aspect of the fibre-reinforced materials, even though lately similar experiments have been carried out on fibrereinforced concretes too.[29]
B A
C
O
D
COD
Figure 3.4: Typical P-COD curve of the splitting tests[30] Looking at the typical load-crack opening curves (P-COD, Figure 3.4[30] ) obtained with the indirect tension tests including the steps following the maximum load phase, it is possible to identify four different phases described as follows: • OA part - Pre-cracking phase: As in the case of the response observed in the uniaxial tension tests, a clearly linear phase is observed in the pre-cracking regime up to a value of approximately 85% of the value of maximum load (Pmax ). • AB part - Nonlinear pre-peak phase: When the first crack is formed (point A, Figure 3.4, Figure 3.5(a)) begins a part where the response is nonlinear due to the loss of concrete [29]
Su-Tae Kang, Jung-Jun Park, Gum-Sung Ryu, Gyung-Taek Koh, and Sung Wook Kim. “Comparison of Tensile
Strengths with Different Test Methods in Ultra High Strength Steel-Fiber Reinforced Concrete (UHS-SFRC)”. in: Key Engineering Materials 417-418 (2009), pp. 649–652. issn: 1662-9795. doi: 10.4028/www.scientific.net/KEM. 417-418.649. [30] Sergio Carmona and Antonio Aguado. “New model for the indirect determination of the tensile stress–strain curve of concrete by means of the Brazilian test”. In: Materials and Structures 45 (Oct. 2012). doi: 10.1617/s11527012-9851-0.
50
Index > 3 Mechanical properties > 3.1 Mechanical properties of the composite stiffness. This part extends until the maximum load is reached. The pre-peak behaviour of the concrete submitted to the brazilian test can be analyzed by means of a strut-andtie model Figure 3.5). Two struts transmit the compression formed because of the loads applied vertically, while two ties placed in the direction orthogonal to the load balance the equilibrium. OAB
BC
(a)
(b)
CD
(c)
(d)
Figure 3.5: (a) Strut-and-tie model used for a pre-cracking regime; (b) Propagation of cracking in a post-peak regime; (c) Final cracking state of the specimen; (d) Strut-and-tie model for the final cracking state of the cylinder[30]
• BC-Softening part: After reaching the maximum load (point B), the load gradually decreases, while the crack opens and extends along the entire section (Figure 3.5(b)). Unlike what is observed in direct tension or in bending tests, the load does not decrease to a null value where the stresses are no longer able to transmit between the open sides of the crack.
• CD-Plateau part: The cracks are now spread throughout the length of the loaded section and near the loading area wedges appear (Figure 3.5(c)). The two halves of the specimen continue the separation phase and by this time undergo a compression load of about 40% of the peak load giving rise to the plateau observed at the end of the curve. The specimen at this point is completely divided and it makes no sense to talk about tension along the two sides of the crack. The new model of analysis should therefore be made according to the new situation. 51
Index > 3 Mechanical properties > 3.1 Mechanical properties of the composite 3.1.3.3
Indirect tension tests - three point bending
The bending test is certainly the most common for its relative ease of execution, because it is representative of many practical situations and because it puts in better evidence the ductility brought by the fibrous reinforcement, more than it happens in the previous tests. The purpose of this test is the determination of the toughness brought by the fibres to the concrete.
A F F
150
A 25
hsp
75 250
250
25
75 150
section A-A
550 x≤5 1
3 y≤5
Dimensions in millimetres 1 Detail (notch) 2 Transducer (clip gauge) 3 Knife edge
2
Figure 3.6: Setup for measuring of the CMOD in a three point bending test of notched specimen[31]
The specimen is positioned on two points, and is loaded in one or two points: in the first case we talk about Three Point Bending Test (3PBT), in the second of Four Point Bending Test (4PBT). The load test on three points foresees that the beam is loaded in half span, while for the four-point the beam is divided into three parts of equal length. The three-point test is performed according to the specifications given in EN 14651 - Test method for metallic fibered concrete - Measuring the 52
Index > 3 Mechanical properties > 3.1 Mechanical properties of the composite flexural tensile strength (limit of proportionality (LOP), residual)[31] as shown in Figure 3.6 and in Figure 3.8. In Figure 3.7[32] is shown a typical machine for running the three point bending test on a notched beam.
Figure 3.7: Machine for three point bending test on notched specimen[32] From the test is obtained the tensile strength for residual flexure fR, j according to this relation: fR, j =
3 · Fj · l 2·b·
h2sp
Equation 3.1[31]
where: fR, j is the residual tensile strength for flexure for CMOD = CMOD j [MPa] (CMOD - Crack Mouth Opening Displacement) with i = 1,2,3,4 corresponding to crack openings equal to 0.5, 1.5, 2.5 and 3.5 mm, respectively (Figure 3.9); Fj is the load for CMOD = CMOD j [N]; l is the span equal to the distance between the supports [mm]; [31]
EN 14651 - Test method for metallic fibered concrete - Measuring the flexural tensile strength (limit of pro-
portionality (LOP), residual). European Committee For Standardization. Rue de Stassart, 36 - B-1050 Brussels, 2005. [32]
Carlos G. Berrocal, Ingemar Löfgren, Karin Lundgren, Niclas Görander, and Christopher Halldén. “Characteri-
sation of bending cracks in R/FRC using image analysis”. In: Cement and Concrete Research 90 (2016), pp. 104–116. issn: 0008-8846. doi: https://doi.org/10.1016/j.cemconres.2016.09.016.
53
Index > 3 Mechanical properties > 3.1 Mechanical properties of the composite b is the width of the specimen [mm]; hsp is the distance between the point where the notch ends and the top surface of the specimen (125 mm).
LVDT 20mm Reference Rod
Hinge
Roller
LVDT 10mm
Extensometer
Notch
Figure 3.8: Setup of three point bending test on notched specimen[31]
In case of materials with high fibre content, where hardening behaviour can be obtained, the tension behaviour must be determined by direct tension tests on unnotched specimens. Load FL F1 F2 F3 F4
CMOD (mm) 0
CMOD1 = 0,5
CMOD2 = 1,5
CMOD3 = 2,5
CMOD4 = 3,5
Figure 3.9: F-CMOD graph for FRC[31] Bending tests on 3 points of notched beam were carried out in the laboratory of material testings of the University of Bergamo with the collaboration of Davide Sirtoli and with the technical assistance of Daniele di Marco. 54
Index > 3 Mechanical properties > 3.1 Mechanical properties of the composite 3.1.3.4
Indirect tension tests - four point bending
P
a
h
h+a=l
P
l
l
l
L=4 l
Figure 3.10: Four point bending test on notched specimen[10]
According to fib Model Code for Concrete Structures 2010, if the result of the bending test on notched specimen is of hardening type, it is necessary to repeat the test on unnotched specimen to verify the real ductility in the absence of notch. It is therefore foreseen the possibility to carry out bending tests on four points on unnotched beams according to UNI 11188 - Elementi strutturali di calcestruzzo rinforzato con fibre d’acciaio - Progettazione, esecuzione e controllo[33] (Figure 3.11).
P
h
P
l
l
l
Figure 3.11: Four point bending test on unnotsched specimen[10]
[33]
UNI 11188 - Elementi strutturali di calcestruzzo rinforzato con fibre d’acciaio - Progettazione, esecuzione e
controllo. Italian. Ente Nazionale Italiano di Unificazione. UNI, Mar. 2007.
55
Index > 3 Mechanical properties > 3.1 Mechanical properties of the composite
Uni-axial response
Flexural response Deflection hardening
Strain hardening Stress
Load
HPFRC
Multiple cracking Matrix cracking
Localization
FRC & HPFRC
Multiple cracking Matrix cracking
Deflection
Strain / Deformation Tension softening
Deflection softening Single crack Matrix cracking
Load
Stress
Single crack Localization FRC Concrete
FRC Concrete
Strain / Deformation
Deflection
Figure 3.12: Tensile and flexural behaviour[12]
3.1.3.5
Wedge Splitting Test
A good test, to be univocally accepted and widely used should have some basic requirements: produce reliable results using preferably small specimens easy to handle and do not require advanced and excessively expensive test systems. The Wedge Splitting Test developed by Brühwiler and Wittmann (1990),[34] satisfies these basic requirements and can also be used by small and medium enterprises in their daily production without having to invest in expensive test equipment. The test configuration is based on the use of specimens usually of prismatic geometry; Other possible geometries are shown in Figure 3.13. Characteristic of the test is however the carving of a rectangular groove at the top of the specimen and a notch (cut-in) below that. The dimensions of the two notches are defined in such a way as to create a vertical fracture in the central part of the specimen. The test preparation foresees that the specimens are placed on a linear support fixed on the base plate of the test machine. Two loading devices equipped with rollers are applied to the [34]
E. Brühwiler and F. H. Wittmann. “The wedge splitting test, a new method of performing stable fracture
mechanics tests”. In: Engineering Fracture Mechanics 35.1-3 (1990), pp. 117–125. issn: 0013-7944. doi: https: //doi.org/10.1016/0013-7944(90)90189-N.
56
Index > 3 Mechanical properties > 3.1 Mechanical properties of the composite upper part of the specimen and a wedge-shaped rigid steel profile, connected directly to the test machine, is placed inside the groove produced previously. The test is ready to be performed; The wedge is pushed downwards by the equipment that will apply a vertical force.
steel loading device with roller bearings groove (cast) starter notch (cut-in)
actuator load cell
Clip gauge wedging device
cube specimen
linear support
Figure 3.13: Wedge Splitting Test setup[12]
The crack opening values are measured by means of transducers. The aim of the test is to measure the fracture energy required to divide the specimen into two halves. This energy is represented by the area below the stress-opening curve of the crack. Tests of this type normally present some difficulties, such as the small deformations at the breaking of the concrete element and the rigidity of the specimens in relation to that of the test machine. However, the use of wedges leads to the overcoming of these problems.
Given the nature of the test, after the test is performed, it is necessary to perform a reverse analysis in order to determine the characteristics of the material.[35] This analysis consists of three main parts: 1. The analysis of data obtained from laboratory tests or on site; 2. The simulation of the test according to the parameters to be determined; [35]
Jan Skoček and Henrik Stang. “Inverse analysis of the wedge-splitting test”. In: Engineering Fracture Mechanics
75.10 (2008), pp. 3173–3188. issn: 0013-7944. doi: https://doi.org/10.1016/j.engfracmech.2007.12.003. url: http://www.sciencedirect.com/science/article/pii/S0013794407004389.
57
Index > 3 Mechanical properties > 3.2 Mechanical properties of the composite 3. An optimization process to minimize the discrepancies between the test data and the corresponding data obtained from the simulation. Many approaches have been developed over the last few decades so to obtain fracture properties; Approaches that in general can be divided into two main groups. The first group includes those methods that use a step-by-step reverse analysis where the point on the softening curve is obtained by minimizing the difference between the calculated load and the actual load measured for the crack opening investigated. Among these methods should be cited the poly-linear method whose advantage lies in its generality, no hypothesis must be done in the pre-experiment phase. On the other hand the determined relationship is strongly influenced by errors of measurement at every point.
3.1.3.6
Double Edge Wedge Splitting Test
A mechanical behavior characterization test, specially proposed for the fibre-reinforced concrete, is the Double Edge Wedge splitting test - DEWS test.
3.1.3.7
Pull-out test
Another test for fibre-reinforced concrete is the pull-off test of a fibre or Pull-out Test.
3.1.4
Behaviour at high temperatures
Regarding the residual performance as a result of exposure to high temperatures, HPFRC materials have interesting mechanical characteristics. The experimental program illustrated by Caverzan, Colombo, Di Prisco, and Rivolta in “High Performance steel fibre reinforced concrete: residual behaviour at high temperature”[36] has envisaged the exposure to high temperatures of cementitious composites containing 100 kg/m3 of short fibres high in carbon (V f = 1.2%). The specimens, characterized by a hardening behaviour at the reference temperature (20 °C), exhibited similar hardening characteristics up to exposure levels equal to 400 °C. [36]
Alessio Caverzan, Matteo Colombo, Marco Di Prisco, and B Rivolta. “High Performance steel fibre reinforced
concrete: residual behaviour at high temperature”. In: Materials and Structures 48 (Nov. 2014). doi: 10.1617/ s11527-014-0401-9.
58
Index > 3 Mechanical properties > 3.2 Characterization of the adherence between HPFRC and plain concrete
3.2
Characterization of the adherence between HPFRC and plain concrete
The characterization is done by the following tests.
3.2.1
Four point jacketed beam bending test 150x150x600 mm concrete beam C20/25
20 mm thick HPFRC jacket
Figure 3.14: Plain concrete beam and HPFRC jacket geometry[20] A preliminary investigation is carried out in order to define the procedure for applying the strengthening layer in HPFRC. Particular attention is paid to the control of the adherence between the concrete without fibres and the jacket in fibre-reinforced material.
150 20
170
150
75
75
450 600
20
Figure 3.15: Load pattern on a jacketed specimen[20] 59
190 150
20
Index > 3 Mechanical properties > 3.2 Characterization of the adherence between HPFRC and plain concrete For this purpose, a series of tests on 150 x 150 x 600 mm specimens made with concrete of class C20/25, is initially carried out. In order to obtain the maximum bond between the plain concrete substrate and the fibre-reinforced jacket, the lateral and lower surfaces of the beams are submitted to a sandblasting operation. This operation increases the roughness of the surfaces and improves the adherence between the two materials. Before casting the material, the surfaces of the beams are wetted. A layer of 20 mm of HPFRC material is cast into a steel mould that covers the lateral and lower surface of the fibre-free concrete beam. The material is compacted by vibrating the mould from the outside. In Figure 3.14 is shown the geometry of a jacketed specimen.
Spherical hinge
HE100 profile
Specimen Loading point
Roller Hinge
HE120 profile
Figure 3.16: Loading machine for a four point bending test of a jacketed specimen[20] The adherence between HPFRC and the non-fibre-reinforced concrete is controlled by performing four points bending tests of jacketed beams. The specimen is arranged as shown in Figure 3.15. The steel machine in which the tests are carried out (Figure 3.16) consists of two steel profiles, one for the support and the other for loading. The upper element, which is used for the distribution of the load, consists of a HE100 profile, appropriately stiffened in the load transfer areas. Between this profile and the test machine there is a spherical hinge that has the function of avoiding any 60
Index > 3 Mechanical properties > 3.2 Characterization of the adherence between HPFRC and plain concrete eccentricity on the specimen during the test. The bottom element, a HE120 profile, is anchored directly to the test machine. The two loading points are made of two knives welded to the plates that can slide on the lower part of the HE100 profile. The two supports are made to simulate a hinge-roller condition. An appropriate number of measurement devices (LVDT-s) are used to monitor the applied load and displacement. In each test 7 measurement devices are used: • 1 load cell which is the load cell of the test machine;; • 2 LVDT transducers to measure the vertical displacement in the middle, front and back of the specimen; • 4 LVDT transducers to measure the crack openings between the substrate and the HPFRC jacketing. 120
HPFRC jacketed specimen
Load [kN]
100
Plain concrete specimen
80 60 40 20 0 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
Split front [mm]
Figure 3.17: Load -crack split front relation for plain concrete and HPFRC jacketed specimens[20] The test is carried out by setting the displacement speed of the actuator at a constant rate of 0.01 mm/s. The beams show a linear behaviour up to 85 kN loading [20] , moment when the micro-cracks begin to form. The opening of micro-cracks is hindered by the presence of fibres, therefore, while a slight decrease in the slope of the curve is noted, the load continues to rise. At this stage there is a hardening behaviour of the material that ensures structural stability even after the first cracks. The maximum load is about 115 kN [20] , when there is the opening of a vertical macro-crack and 61
Index > 3 Mechanical properties > 3.2 Characterization of the adherence between HPFRC and plain concrete the breaking of the specimen. From this moment, the future cracks that characterize the unloading phase, are concentrated in the macro-crack. During the softening (strain softening) behaviour, the gradual opening of the macro-crack occurs and the fibres are progressively extracted from the matrix or yielded. Figure 3.17 shows the split between the plain concrete and the HPFRC jacket.
3.2.2
Substrate - HPFRC adherence tests
In this paragraph the adherence between the substrate of plain concrete and the strengthening material in HPFRC will be studied. The bonding capacity between existing concrete and repair concrete plays an important role in the validity of this strengthening method. If a sufficient adherence is obtained, the strengthening part behaves in a monolithic way. A good bond between substrate concrete and repairing material in HPFRC is strictly dependent on the method adopted for the preparation of the contact surfaces.[37] A widespread practice for the removal of the damaged layer from the structural element to be strengthened is the hammer usage for cleaning. It is believed that this method promotes damages to the substrate causing micro-cracks which in turn cause a further weakening of the element to be strengthened. The operations of sandblasting and water jet instead, are the best methods of preparation of the surface both to obtain better adherencess than to avoid damaging the structural element.[38][39][40][41][42]
To achieve a high adherence, the substrate surface should be wetted for at least 24 hours before the new concrete is cast. The level of humidity of the substrate may be critical in reaching the bond. A dry substrate could absorb too much water from the repair material while excessive humidity in the substrate could clog the pores and prevent the absorption of the repair material. As a result, a [37]
Pedro Santos, Eduardo Nuno Brito Santos Júlio, and Vitor Dias da Silva. “Correlation between concrete-to-
concrete bond strength and the roughness of the substrate surface”. In: Construction and Building Materials 21.8 (Aug. 2007), pp. 1688–1695. issn: 0950-0618. doi: https://doi.org/10.1016/j.conbuildmat.2006.05.044. [38] Eduardo Nuno Brito Santos Júlio, Fernando Branco, and Vitor Dias da Silva. “Concrete-to-concrete bond strength. Influence of the roughness of the substrate surface”. In: Construction and Building Materials 18 (Nov. 2004), pp. 675– 681. doi: 10.1016/j.conbuildmat.2004.04.023. [39] Francois Saucier and Michel Pigeon. “Durability of New-to-Old Concrete Bondings”. In: Special Publication 128 (Jan. 1991), pp. 689–705. doi: 10.14359/2066. [40] Johan Silfwerbrand. “Improving concrete bond in repaired bridge decks”. In: Concrete International 12 (Sept. 1990), pp. 61–66. [41] Kal R. Hindo. “In-Place Bond Testing and Surface Preparation of Concrete”. In: Concrete International 12 (Jan. 1990). [42] A. I. Abu-Tair, S. R. Rigden, and E. Burley. “Testing the Bond between Repair Materials and Concrete Substrate”. In: Materials Journal 93 (Jan. 1996), pp. 553–558. doi: 10.14359/9861.
62
Index > 3 Mechanical properties > 3.2 Characterization of the adherence between HPFRC and plain concrete substrate with saturated pores but with a dry surface is considered the best solution. A good bond between substrate and strengthening material can also be obtained without wetting the surfaces but making use of Epoxy Primer. The tests to determine the bonding between the concrete substrate and the repair material can be divided into different categories. The first testing category measures the adherence under tension, tensile stress. The tests belonging to this category are: Pull-off, direct tension and splitting. The second testing category measures the adherence under shear stress. Several tests belong to this category including the one L-shaped, mono-superficial shear. In most cases the adherence surface for a direct shear test is submitted to shear stress and to a small flexure. The third category measures the bonding through combined shear and compression tests. All oblique shear tests fall into this category.
3.2.2.1
Direct tension test for the adherence 30 mm thick HPFRC layer
100 x 100 x 150 mm plain concrete prisms
Figure 3.18: Geometry of specimens in direct tensile bond test for adherence[20] In the direct tension test the force is transmitted to the specimen through the spherical hinges and the steel plates (Figure 3.19) glued to the specimen. It is essential a careful alignment of the specimen in the loading axis. Even a very small misalignment would introduce an eccentricity that causes dispersion in the results. During the test the failure can take place in the substrate concrete, in the connection interface between plain concrete - HPFRC layer, or at the epoxy resin used to glue the test plate to the sample. The magnitude of the tensile force and the position of the breaking surface provide information on the performance of the strengthening system. When the failure takes place in the interface between the two materials, the test provides a correct indication of the strength of adherence. In this case, the final load is a direct measure of the adherence be63
Index > 3 Mechanical properties > 3.2 Characterization of the adherence between HPFRC and plain concrete tween the HPFRC and the non-reinforced concrete substrate. The failure in the concrete substrate for example indicates that the adherence bond is larger than the tensile strength of the plain concrete. The tension test is carried out on a bi-superficial specimen consisting of two concrete prisms of 100 x 100 x 150 mm dimension, between which a layer of self-compacting HPFRC of 30 mm thickness is cast.
Spherical hinge
Epoxy adhesive
Concrete substrate
HPFRC material
Bond regions
Steel plate 100 x 100 mm
Figure 3.19: Set-up for direct tension test for the adherence[20] The procedure for preparing the specimens is as follows: 1. Traditional concrete castings in moulds. 2. Removal of specimens after 24 hours from the casting. 3. Cleaning of specimens from extra dust or particles. 4. Maturation of specimens in water for 28 days. 5. Removal from the environment of maturation and sandblasting of the two interface surfaces by removing a very thin layer in order to have an irregular surface. 6. Cleaning with metallic brush and high pressure air of the irregular interface surfaces. 7. The HPFRC strengthening material is cast between the two prismatic elements of plain concrete to obtain the result shown in Figure 3.18. 64
Index > 3 Mechanical properties > 3.2 Characterization of the adherence between HPFRC and plain concrete The adherence bond by tensile strength (σDT )[43] is defined by the tensile force (PDT ) divided by the failure surface area (A f DT ) of the specimen: σDT =
3.2.2.2
PDT A f DT
Equation 3.2[43]
Shear test for the adherence
In the shear test for the adherence, the strength is determined by applying shear forces parallel to the connection interface between the plain concrete block and the HPFRC jacket. As the specimen consists of two parts, a flexure moment is generated as the load is applied. To solve this problem, specimens consisting of a block of traditional concrete (150 x 150 x 150 mm) are produced, which is laterally strengthened by a HPFRC jacket of 30 mm thick. The traditional concrete block has the same strength as the concrete used for the direct tensile test in Paragraph 3.2.2.1. 150 x 150 x 150 mm prism of plain concrete
30 mm thick HPFRC jacket
(a)
(b)
Figure 3.20: (a) Geometry of specimen and (b) set-up of the shear test for adherence[20]
Before the casting of the strengthening material in HPFRC, the lateral surfaces of the traditional concrete block are sandblasted and wetted for 24 hours. The treatment used is similar to the one used for the direct tension test. The direct shear test is carried out by applying a compression load on the block of traditional concrete; The load is applied through a steel plate of dimensions 120 x 120 x 20 mm. A 5 mm [43]
Alberto Carpinteri. Scienza delle Costruzioni. Italian. 2nd ed. Collana di Ingegneria Strutturale. Pitagora, 1993.
isbn: 9788837105297. url: https://books.google.it/books?id=%5C_wQuAAAACAAJ.
65
Index > 3 Mechanical properties > 3.3 Bond in tension - Simplified models thick neoprene layer is applied between the specimen and the steel plate to improve the contact between the two elements. A 20 mm thick steel frame is used to support the HPFRC jacket. The adherence bond by shear stress (σST ) is determined by the compression force (PST ) divided by the failure surface area (A f ST ) of the specimen:
σST =
PST A f ST
Equation 3.3[43]
For further detail see: Abdel Zaher, Kunieda, Ueda, and Nakamura (2008)[44] , Bonaldo, Barros, and Lourenço (2005)[45] , Momayez, Ehsani, Ramezanianpour, and Rajaie (2005)[46] , Silfwerbrand (2003),[47] Austin, Robins, and Pan (1999)[48] , Perez, Morency, Bissonnette, and Courard (2009)[49] , Tschegg and E. Stanzl (1991)[50] , Li (2003)[51] .
3.3
Bond in tension - Simplified models
From the bending tests it is possible to obtain two stress-crack opening simplified constitutive relations: a rigid-plastic post-cracking behaviour and a linear behaviour (hardening or softening), [44]
Ahmed Abdel Zaher, Minoru Kunieda, Naoshi Ueda, and Hikaru Nakamura. “Evaluation of crack opening
performance of a repair material with strain hardening behavior”. In: Cement and Concrete Composites 30 (Nov. 2008), pp. 863–871. doi: 10.1016/j.cemconcomp.2008.08.003. [45] Everaldo Bonaldo, Joaquim Barros, and Paulo Lourenço. “Bond characterization between concrete substrate and repairing SFRC using pull-off testing”. In: International Journal of Adhesion and Adhesives 25 (Dec. 2005), pp. 463–474. doi: 10.1016/j.ijadhadh.2005.01.002. [46] A Momayez, Mohammad Ehsani, Ali Ramezanianpour, and H Rajaie. “Comparison of methods for evaluating bond strength between concrete substrate and repair materials”. In: Cement and Concrete Research 35 (Apr. 2005), pp. 748–757. doi: 10.1016/j.cemconres.2004.05.027. [47] Johan Silfwerbrand. “Shear bond strength in repaired concrete structures”. In: Materials and Structures 36 (Jan. 2003), pp. 419–424. doi: https://doi.org/10.1007/BF02481068. [48] Simon Austin, Pei Robins, and Youguang Pan. “Shear bond testing of concrete repairs”. In: Cement and Concrete Research 29 (July 1999), pp. 1067–1076. doi: 10.1016/S0008-8846(99)00088-5. [49] Fabien Perez, Maxim Morency, Benoît Bissonnette, and Luc Courard. “Correlation between the roughness of the substrate surface and the debonding risk”. In: Concrete Repair, Rehabilitation and Retrofitting II (Jan. 2009), pp. 347–348. doi: 10.1201/9781439828403.ch133. [50] Elmar Tschegg and S E. Stanzl. “Adhesive power measurements of bonds between old and new concrete”. In: Journal of Materials Science 26 (Oct. 1991), pp. 5189–5194. doi: 10.1007/BF01143212. [51] Gengying Li. “A New Way to Increase the Long-Term Bond Strength of New-to-old Concrete by the Use of Fly Ash”. In: Cement and Concrete Research 33 (June 2003). doi: 10.1016/S0008-8846(02)01064-5.
66
Index > 3 Mechanical properties > 3.3 Bond in tension - Simplified models as shown in Figure 3.21,[52] where fFts represents the residual serviceability resistance, defined as the post-cracking strength evaluated at crack openings compatible with the serviceability, and fFtu the ultimate residual strength. The tension values, fFts and fFtu , that characterize the two models can be evaluated with ways that will be described later.
σ
σ Post-crack hardening
Rigid-plastic fFtu
fFtu
fFtu
fFts fFtu Post-crack softening wu
W
wu
W
Figure 3.21: Simplified stress-crack constitutive laws[9]
For materials with hardening behaviour, in the presence of multi-cracking, it is not necessary to determine the opening of the cracks because it is possible to operate directly in terms of tensions and deformations.
3.3.1
Rigid-plastic model
According to fib Model Code for Concrete Structures 2010, the rigid-plastic model uses a single reference value, fFtu , based on the ultimate behaviour. The determination of this parameter is based on an equivalence between a distribution of triangular stresses and a uniform distribution in the hypothesis that the entire compression force is concentrated in the upper fibre of the section, as shown in Figure 3.22.
[52]
Xiliang Ning, Yining Ding, Fasheng Zhang, and Yulin Zhang. “Experimental study and prediction model for
flexural behavior of reinforced SCC beam containing steel fibers”. In: Construction and Building Materials 93 (2015), pp. 644–653. issn: 0950-0618. doi: https : / / doi . org / 10 . 1016 / j . conbuildmat . 2015 . 06 . 024. url: http://www.sciencedirect.com/science/article/pii/S0950061815007059.
67
Index > 3 Mechanical properties > 3.3 Bond in tension - Simplified models
fR3
fFtu =
fR3 3
Figure 3.22: Simplified model for residual strength evaluation in tension[9]
Mu =
fR3 · b · h2sp 6
=
fFtu · b · h2sp
Equation 3.4[9]
2
from which is obtained:: fFtu =
fR3 3
Equation 3.5[9]
fR1 and fR 3 are, respectively, the equivalent post-cracking strengths significant for the serviceability limit state and for the ultimate limit state.
3.3.2
Linear elastic model
The linear elastic model identifies two reference values, fFts and fFtu , based on the SLS and ULS behaviour. These values can be defined on the basis of equivalent values of bending strengths with the following expressions: σ = E⋅𝜒⋅x x
y
𝜒
εx = w/lcs (a)
fFts
C
M
M
fFts = 0.45fR1 (b)
0.5fR3 - 0.2fR1 (c)
Figure 3.23: Stress diagrams for residual strength evaluation in tension[9] 68
Index > 3 Mechanical properties > 3.3 Bond in tension - Simplified models
fFts = 0.45 · fR1
Equation 3.6[9]
wu · ( fFts − 0.5 · fR3 + 0.2 · fR1 ) ≥ 0 Equation 3.7[9] CMOD3 where wu is the maximum crack opening accepted in the structural design and depends on the fFtu = fFts −
required ductility. The equation for fFtu and wu = CMOD3 is obtained from the equilibrium in rotation to the ultimate limit state by applying to tensions along the section a stress-block type of distribution, as shown in Figure 3.23(c). The equation for fFtu and wu , CMOD3 is obtained by considering a linear constitutive relation between the abscissa points CMOD1 and CMOD3 , to the abscissa point wu , as shown in Figure 3.24. σ
σN fR1
fFts
fR3
fFtu
CMOD1=0.5 CMOD3=2.5
0.5fR3-0.2fR1
wu CMOD3 w
CMOD [mm]
(a)
(b)
Figure 3.24: (a) Typical results of bending tests with softening behaviour; (b) Linear post-cracking constitutive law[9] The value of the stress corresponding to the crack opening CMOD1 is determined by equilibrium, with the hypothesis that the distribution of compression stresses is linear (Figure 3.23(b)) and the tension behaviour is Elasto-Plastic up to a crack opening corresponding to the serviceability limit state (CMOD1 ): M(CMOD1 ) =
fR1 · b · h2sp
Equation 3.8[9] 6 The stress corresponding to the crack opening CMOD3 is determined by the equilibrium with the hypothesis that the resulting compression stress is applied to the extrados (Figure 3.23(c)) and the behaviour in tension is rigid-linear: M(CMOD3 ) = 69
fR3 · b · h2sp 6
Equation 3.9[9]
Index > 3 Mechanical properties > 3.4 Bond in tension in terms of stress-strain
3.3.3
Orientation effects
The effects of a anisotropic distribution of the fibres can be evaluated by modifying the residual strength values in serviceability ( fFts ) and ultimate limit state ( fFtu ); in particular, known the orientation factor K, is possible to have:
3.4
fFts,mod =
fFts K
Equation 3.10[9]
fFtu,mod =
fFtu K
Equation 3.11[9]
Bond in tension in terms of stress-strain
The relations introduced are expressed in terms of tension-crack opening. In case of materials with softening behaviour, the definition of the stress-strain relation is based on the identification of the width of the crack opening with the variation in length of a suitable base l cs , characteristic of the structural element. Therefore, the deformation can be assumed to be equal to: ε=
w l cs
Equation 3.12[9]
In presence of traditional reinforcement bars, the characteristic length l cs , can be evaluated as:
sr m
l cs = min{sr m, y} φ = ξ 50 + 0.25 · k 1 · k 2 · ρ
Equation 3.13[9] Equation 3.14[9]
where: sr m is the average value of the distance between the cracks; y is the distance of the neutral axis from the tensed edge of the section evaluated in elastic cracked phase neglecting the tensile strength (pre and post-cracking) of the FRC; ξ is a dimensionless coefficient to be assumed to be equal to 1.0 for l f /d f < 50, equal to 50 d f /l f for 50 ≤ l f /d f ≤ 100 and equal to 1/2 for l f /d f > 100; d f is the diameter of the fibres; l f is the length of the fibres; φ is the diameter of the reinforcing bars; k 1 is a coefficient equal to 0.8 for improved adherence or ribbed reinforcing bars and equal to 1.6 for smooth bars; 70
Index > 3 Mechanical properties > 3.4 Bond in tension in terms of stress-strain k 2 is a coefficient equal to 0.5 for simple or composed bending with y ≤ h and equal to 1.0 for tension or composed bending with y > h; h is the height of the section; ρ is the geometric ratio between the area of the reinforcement bars and the area of the tensed part of the section, identified by the distance y. The ultimate tensile strength fFtu in the linear model depends from the required ductility, related to the acceptable crack opening. The ultimate crack opening can be calculated as wu = l cs / εFu , assuming εFu equal to 2% for a variable stress distribution along the section and equal to 1% for a constant stress distribution. The maximum crack opening in any case cannot be higher than 2.5 mm. In the event of sections without traditional reinforcement bars subjected to bending, tension-flexure or compression-flexure with a resultant external to the section itself, the value of sr m is assumed equal to the height of the section. σ
σ Rigid-plastic hardening
fFtu
fFtu
fFts
fFtu
softening
εFu
ε
fFtu
εFu
ε
Figure 3.25: Stress-strain constitutive laws[9]
In case of material with hardening behaviour, the ultimate strain FU value is assumed to be 2% for a variable stress distribution along the section and 1% for a constant stress distribution. A material can be considered hardening when it shows a tensile hardening behaviour of up to εFU = 1%. It is therefore possible to use the simplified models of Figure 3.25 corresponding to the tension-crack opening relations of Figure 3.21.
3.4.1
Tensile stress-strain relationship representation
In the case of more rigorous evaluations, e.g. tracing of the moment-curvature diagrams of compression-flexured sections or numerical analyses it is necessary to define a simplified stressstrain in tension relationship that approximates with sufficient precision the real behaviour of the material. 71
Index > 3 Mechanical properties > 3.4 Bond in tension in terms of stress-strain A suggestion for a possible schematization is reported in fib Model Code for Concrete Structures 2010, where are indicated some possibilities depending on the pre and post-peak behaviour of the material. Regarding the post-peak stage, the ultimate limit state, it is possible to use the constitutive bonds described in Paragraph 3.3. For the pre-peak stage, i.e. the serviceability limit state, three possible cases are distinguished. Case (I)
σ
Case (II)
σ
σC fFts
B
A
Plain Concrete
C
fFtu 0.2fct
fFts fct
A
B
E
fFtu
D
Case (I) εC > ε P εC = ε P
E
fFtu fct B σA A
D
E'
D
fFts 0.9fFts A'
E' fct
Case (III)
σ
Case (II) σD - σ A σB - σ A ≤ εD - ε A εD - ε A
Plain Concrete
Plain Concrete
E Q εP εC εQ εSLS
εULS
ε
εP
εSLS
(a)
εULS
ε
εA
εSLS
(b)
σC < fct σC = fct
εULS
ε
Case (III) σD - σ A σB - σ A > εD - ε A εD - ε A
(c)
Figure 3.26: (a) Stress-strain relations at the serviceability limit state for softening behaviour; (b),(c) For softening or hardening behaviour of the FRC[9]
3.4.1.1
Case I
For materials with softening behaviour up to peak resistance fct , is used the same tensile relation that was employed for non-fibre-reinforced concrete. Point A in the curves in Figure 3.26 (a), (b), (c) is defined in Figure 3.27. In case of non-cracked concrete, the bilinear branch up to the peak tensile strength is defined by the following equations:
OA branch
AB branch
σct = Eci · εct
σct = fctm · 1 − 0.1 ·
for σct ≤ 0.9 fctm 0.00015 − εct
0.00015 − 0.9 ·
Equation 3.15[9]
! for 0.9 · fctm < σct ≤ fctm
fc t m Eci
Equation 3.16[9] where Eci is the tangent elastic modulus in MPa calculated as: Eci = Eco · αE
where: 72
fck + ∆ f 10
13 Equation 3.17[9]
Index > 3 Mechanical properties > 3.4 Bond in tension in terms of stress-strain Eci is the elastic modulus in MPa at 28 days; fck is the characteristic compression strength; ∆ f = 8 MPa; Ec0 = 21.5 103 MPa; αE varies according to the type of aggregate and is equal to: 1.2 for basalt; 1 for quartzite; 0.9 for limestone and 0.7 for sandstone; εct is the tension stress in MPa; fctm is the tensile strength in MPa calculated as:
2
fctm = 0.3 · ( fck ) 3
for concrete of class ≤ C50 2
for concrete of class > C50
Concrete tensile stress σct ≥ 0
Concrete tensile stress σct ≥ 0
fctm = 2.12 · ln (1 + 0.1 · ( fck + ∆ f )) 3
fctm 0.9fctm
Equation 3.18[9]
Equation 3.19[9]
fctm GF = area under the stress-crack opening relation
0.2fctm w1 = GF /fctm
0.15
wC = 5GF /fctm
Crack opening w
Concrete strain εct [‰]
Figure 3.27: Stress-strain and stress-crack opening relations for uniaxial tension[9] In post-cracked phase, a bilinear relation is still applied Figure 3.26(a). The post-peak branch (BC) is analytically identified by the relation: ε − εP σ − fct = 0.2 · fct − fct εQ − ε P
for
ε P ≤ ε ≤ εC
Equation 3.20[9]
with: Gf 0.8 · fct εQ = + εP − fct · l cs Ec
Equation 3.21[9]
where G f is the fracture energy of the unreinforced concrete [N/m]. In the absence of experimental data, for ordinary concrete, it can be calculated as: 73
Index > 3 Mechanical properties > 3.4 Bond in tension in terms of stress-strain
0.18 G f = 73 · fcm
Equation 3.22[9]
where fcm is equal to the average cylindrical compression strength in MPa. For materials with softening behaviour, residual resistance (fourth branch) is defined by two points corresponding to (εSLS, f Fts) and (εU LS, fFtu ), where: CMOD1 l cs wu 2.5 = = min εFu, l cs l cs εSLS =
εU LS
Equation 3.23[9] Equation 3.24[9]
with: εFu = 2% for a variable deformation distribution along the section and 1% for a tension-only distribution of deformations. The first and second branch suggested in the part of the pre-cracking curve and the branch after reaching of the peak correspond to the behaviour of the unreinforced concrete to the intersection with the residual post-cracking behaviour which takes into account the presence of fibres. When this condition is not applicable, a new second branch is proposed, as shown in Figure 3.26 (b) e (c). For materials characterized by a stable crack propagation up to εSLS with a strength fFts greater than fct , two cases can be considered: 3.4.1.2
Case II
The process of cracking is stable up to the deformation εSLS and the bond is still represented by four branches. The first two remain those of the corresponding unstrengthened concrete, while the third branch (BD) is described analytically as: ε − εP σ − fct = fFts − fct εSLS − ε P 3.4.1.3
ε P ≤ ε ≤ εSLS
for
Equation 3.25[9]
Case III
The process of cracking is stable up to the deformation εSLS and the bond is still represented by three branches. The second branch (A’D) is defined as: σ − σA0 ε − ε A0 = 0 fFts − σA εSLS − ε A0
ε A0 ≤ ε ≤ εSLS
for
74
Equation 3.26[9]
Index > 3 Mechanical properties > 3.4 Bond in tension in terms of stress-strain where: σA0 is on the elastic branch and corresponds to a stress equal to 0.9 fFts . In both cases (II) and (III), the material may be softening (DE) or hardening (DE’) depending on the slope of the last branch.
75
Index > 3 Mechanical properties > 3.4 Bond in tension in terms of stress-strain
76
Chapter 4
Applications 4.1
Basic concepts regarding strengthening operations with HPFRC
In this paragraph will be discussed the design at the Ultimate Limit State and design strengths.
4.1.1
Ultimate limit state
The design at ULS of structures subject to bending requires the evaluation of the ultimate resistant moment and the comparison with the design moment. The essential hypotheses on which the analysis is erected for sections of concrete strengthened with jackets or layers of FRC are these: • Preservation of the condition of flat sections till failure, in order to ensure that the graph of the normal deformations is linear; • Perfect continuity between fibre-reinforced concrete and traditional concrete and between fibre-reinforced concrete and reinforcing bars, if present; • Constitutive bond of the fibre-reinforced concrete; • Constitutive bond of the traditional concrete and, if present, of the reinforcement bars complying to the current laws. It is assumed that failure by bending occurs when one of the following conditions is met: • Achievement of the maximum compression deformation in traditional concrete; 77
Index > 4 Applications > 4.1 Basic concepts regarding strengthening operations with HPFRC • Achievement of maximum compression deformation in fibre-reinforced concrete. Regarding the compression behaviour of traditional concrete but also of reinforced concrete, it is possible to use the simplified tension-deformation diagrams indicated by the current norms.[53] .
σ
σ
f cd
σ
f cd
εc2 εcu ε
f cd
εcu ε
εc3
(a)
(b)
εc4
52
εcu ε (c)
Figure 4.1: Stress-strain models for compressed concrete: (a) parabola-rectangle; (b) trianglerectangle; (c) stress-block[53]
For design and verification formulas it is considered a stress-block type of bond in which the deformations εc4 and εcu are defined as follows:
• Class lower than C50/60: εcu = 3.5‰; εc4 = 0.7‰ • Class higher than C50/60: εcu = 2.6‰+ 35‰[(90 - fck )/100]4 ; εc4 = 0.2εcu • Achievement of the maximum tensile deformation in reinforcing steel bars, if present; • Achievement of the maximum tensile deformation in fibre-reinforced concrete.
4.1.2
Design strengths
The tests of the fibre-reinforced elements must be made both in compliance with the serviceability limit states (SLS), as well as in respect of the ultimate limit state (ULS), as defined in Decreto del Ministero delle infrastrutture 14 gennaio 2008 - Approvazione delle nuove norme tecniche per le costruzioni (2008). By means of the partial coefficients method it is necessary to verify that, using the project values of actions, stresses and resistances, in any project context, no [53]
Ministero delle infrastrutture, Ministero dell’Interno, and Il capo dipartimento della protezione civile. Decreto del
Ministero delle infrastrutture 14 gennaio 2008 - Approvazione delle nuove norme tecniche per le costruzioni. Italian. Supplemento Ordinario n. 30. Ministero delle infrastrutture. Roma, Italia: Gazzetta Ufficiale della Repubblica italiana, Feb. 2008. 654 pp.
78
Index > 4 Applications > 4.1 Basic concepts regarding strengthening operations with HPFRC limit state is violated. So it must be:
Ed ≤ Rd
Equation 4.1[53]
where Ed and Rd project values of the effect considered and the corresponding strength within the limit state examined, respectively. The project values are obtained from the characteristic ones by means of appropriate partial coefficients, whose values, for the various limit states, are those indicated in the norms in force properly integrated with regard to the tensile strength of the fibre-reinforced concrete. The values related to the properties of the materials used in the design of fibre-reinforced structures must have been identified by standardized laboratory tests. The mechanical properties of materials, strength and strain are determined by the corresponding characteristic values, as identified afterwards. Only the rigidity parameters of the materials, the modules of elasticity, are evaluated by their respective average values. The project value of the generic resistance property, X d , can be expressed in an overall way by an expression of this kind: Xd =
Xk γm
Equation 4.2[53]
where γm is a partial coefficient of the material and Xk is the characteristic value of the generic property. For the ultimate limit states, a value of 1.5 is generally adopted, however, in the case of high quality control over the material, for example the resistances are obtained with specific structural tests, it is possible to adopt a coefficient γF equal to 1.3. For the serviceability limit states it is suggested to assign a unitary value to each of the partial coefficients. For design and verification formulas, reference is made to these values: • fcd of the traditional concrete, design compressive strength; • fyd of the reinforcing bars, design yield strength; • fF cd of the fibre-reinforced concrete, design compressive strength; • fFt d of fibre-reinforced concrete, design tensile strength. In Table 4.1 are listed the values used in analytical expressions, highlighting three possible cases: 79
Index > 4 Applications > 4.1 Basic concepts regarding strengthening operations with HPFRC • New design and verification of a FRC strengthened section, in which are used for the traditional concrete and the steel, the values of the design strengths obtained by dividing the characteristic strengths ( fck and fyk ) for the respective coefficients on the materials (γc = 1.5 and γs = 1.15) indicated in Decreto del Ministero delle infrastrutture 14 gennaio 2008 - Approvazione delle nuove norme tecniche per le costruzioni and for the FRC material the design strengths obtained by dividing the characteristic strengths by the coefficients γF =1.5 or 1.3 in the case of good quality control over the material;
• Design and verification of strengthening in FRC for the existing sections in reinforced concrete, in which are used for the traditional concrete and steel the values of the resistances obtained by dividing the average resistances for the respective confidence coefficients (FC) indicated in Circolare 2 febbraio 2009, n. 617 - Istruzioni per l’applicazione delle "Nuove norme tecniche per le costruzioni" di cui al decreto ministeriale 14 gennaio 2008.[54] If the failure mechanism at the ultimate limit state is ductile, it is not strictly necessary to apply additional coefficients, whereas if the mechanism were to be of fragile type the values of the resistances of the materials should be subsequently divided by γc and γs factors. It is suggested to do in any way the above-mentioned reduction in favour of safety. What is stated in the previous point applies to the FRC material;
• Validation of the analytical expressions through comparison with experimental test results, in which the average values of the resistances are used for each of the materials ( fcm ; fγm ; fF cm ; fFtm ).
In the design phase, with regard to the FRC material, the characteristic value of the compressive strength fF ck could be considered equal to 90 MPa at most: using the above value it is not necessary to ask for authorization to the CSLLPP. That authorization will be needed in the case higher values were to be wanted. In contrast, the nominal value of the compressive strength fF cm can be greater.
[54]
Ministero delle infrastrutture e dei trasporti. Circolare 2 febbraio 2009, n. 617 - Istruzioni per l’applicazione
delle "Nuove norme tecniche per le costruzioni" di cui al decreto ministeriale 14 gennaio 2008. Italian. Supplemento Ordinario n. 27. Ministero delle infrastrutture e dei trasporti. Roma, Italia: Gazzetta Ufficiale della Repubblica italiana, Feb. 2009. 447 pp.
80
Index > 4 Applications > 4.2 Application phases Strength
Design
considered
strength
Characteristic
Coefficient
Average Original concrete
Newly
fck
fcd = 0.85 fck /γc
Compression
γc = 1.5 FC = 1 level of knowledge LC3
Existing
fcm
fcd = 0.85 fcm /(FCγc )
section
FC = 1.2 level of knowledge LC2 FC = 1.35 level of knowledge LC1* γc = 1.5
fcd = fcm
Experimental tests
Fibre-Reinforced Concrete Newly
fF ck ≤ 90 MPa
fF cd = 0.85 fF ck /γF
Compression
γF = 1.5 (o 1.3 for good material controls)
Experimental
fF cm
fF cd = fF cm
tests Newly
fFtk
fFt d = fFtk /γF
Tension
γF = 1.5 (o 1.3 for good material controls)
Experimental
fF cm
fFt d = fFtm
tests Reinforcement bars Newly
fyk
fyd = fyk /γs
γs = 1.15
Tension / FC = 1 level of knowledge LC3 Compression Existing
fym
fyd = fym /(FCγs )
section
FC = 1.2 level of knowledge LC2 FC = 1.35 level of knowledge LC1* γs = 1.15
Experimental
fym
fyd = fym
tests
Table 4.1: Strength values of materials used in design and verification formulations[53]
4.2
Application phases
In the following paragraphs the application phases of jacketing with HPFRC will be discussed.
4.2.1
Preparation of the support
The application of the HPFRC material jacket, which is carried out by casting the strengthening material directly on the original concrete, must be anticipated by the preparation of the support of the elements to be strengthened. Several techniques can be used for the preparation of surfaces: scarification, sandblasting, hammering, chiseling. The aim is to remove degraded portions and achieve a high level of roughness with the in order to increase the adherence bond between the surfaces of the two 81
Index > 4 Applications > 4.3 Applying the strengthening technique materials. Researches carried out in the last decades have shown that a surface irregularity of 2-3 mm is enough to ensure a good adhesion between substrate and fibre-reinforced concrete. After the surface preparation operation, the support should be subject to aspiration and hydrowashing to eliminate any leftover dust.
4.2.2
Positioning of metal net meshes
Later on, it is the possible to place and fix by tessellation net meshes in harmonic steel or electrowelded ones. If the placement of the net foresees the use of several parts, those should be correctly overlapped.
4.2.3
Support saturation
Before making the casting of the jacket in HPFRC material, it is necessary to wet the surfaces of the members to be strengthened until the support is saturated. If thixotropic concrete is used, it is convenient to apply {glsprimer or other adhesives for the increase of the adherence.
4.2.4
Jacket casting
In case of strengthening with pourable HPFRC material, very high sealing formworks are positioned and the casting is done by simple pouring. Should the consolidation be performed with thixotropic HPFRC material, the application is executed through the use of trowel without the help of formworks. Near the casting restart is necessary to insert a wire mesh to ensure the structural continuity of the strengthening.
4.3
Applying the strengthening technique
In the following paragraphs will be seen in detail the applications of reinforcement with HPFRC jackets of different structural elements.
4.3.1 4.3.1.1
Strengthening of floors The making of floor diaphragms
The weakness of structures in masonry is most often related to the off-plan rotation of perimeter walls. Perimeter walls should be properly tied together to prevent this collapse mechanism. A possible technique for the construction of a building with box behaviour considers the use of 82
Index > 4 Applications > 4.3 Applying the strengthening technique perimetric chains: However, the efficiency of this configuration could be lowered in cases of high span/thickness ratios of the walls. The construction of floor diaphragms connected with rigid perimeter walls is a valid alternative solution capable of ensuring an adequate transfer of horizontal actions[55][56] (Figure 4.2[57] ).
(a) Façade overturning
(b) Lateral wall overturning
(c) Diaphragm arch excessive rocking
(d) (e) Floor Box and Roof Box structures preventing perimeter walls overturning
Figure 4.2: Some seismic failure mechanisms[57] In numerous buildings in masonry there are wooden floors, or when there are slabs with a mixed structure with steel beams or attics in concrete-and-masonry, most of the time these are made without an appropriate upper hood in reinforced concrete: in both cases there are no floor diaphragms sufficiently rigid or adequate. In cases of reinforced concrete structures in most of the times the increase in performance with respect to seismic loads is assured by the construction of sismo-resistant walls: In this case it is advisable that the floor diaphragm is rigid enough and effectively connected to the walls in order to ensure the transfer of seismic actions. In the above mentioned contexts, the strengthening of floors is transformed into a dutiful op[55]
Cristina Zanotti, Alessandra Marini, and Giovanni Plizzari. “Nonlinear FE analysis of fiber reinforced concrete
floor diaphragms undergoing horizontal seismic actions”. In: (June 2009). [56] Cristina Zanotti. “Thin Fiber Reinforced Concrete floor diaphragms for the seismic enhancement of existing buildings”. In: Proceedings of the 8th fib International PhD Symposium in Civil Engineering, 20-23 June 2010, Kgs Lyngby, Denmark. Ed. by Gregor Fischer, Mette Rica Geiker, Ole Hededal, Lisbeth M. Ottosen, and Henrik Stang. Lyngby, Denmark: Technical University of Denmark, Departments of Civil Engineering, June 2010. isbn: 978-87-7877-301-2. [57] Ezio Giuriani and Alessandra Marini. “Experiences from the Northern Italy 2004 earthquake: Vulnerability assessment and strengthening of historic churches”. In: Proceedings of the VI International Conference on Structural Analysis of Historic Construction, SAHC08, 2-4 July 2008. Bath, United Kingdom: CRC Press - Taylor and Francis Group, July 2008, pp. 13–24. isbn: 978-1-4398-2822-9. doi: 10.1201/9781439828229.ch2.
83
Index > 4 Applications > 4.3 Applying the strengthening technique eration for the improvement or adaptation of the behaviour of the buildings with respect to the seismic loads. In this context, the organization of the deck is of primary importance. Subjected to the actions in their own plane, the diaphragms can be designed similar to high beams in which the curbs are the wings and the panel is the core, based on the idea that the bending moments and the shear actions are assigned respectively to the curbs and to the core panel. For a good transfer of the horizontal actions inside the diaphragm and from the diaphragm to the sismo-resistant members, the core panel should be effectively armed and on the perimeter curbs and pilasters must be present and reinforced too.
4.3.1.2
Strengthening of RC floors
Among the solutions developed in the past for the construction of rigid decks, an economic and effective technique usually used considers, beyond the realization of curbs and pilasters, the casting of a slab in RC and reinforced with a steel mesh. To ensure compliance with the minimum concrete cover of the net mesh, the thickness of the diaphragm is usually larger than 5 cm. This causes a considerable increase of the masses and, consequently, of the seismic stresses, not mentioning the significant increases in the thickness of the deck, with subsequent problems on the variations of the height of the thresholds in the rooms of the buildings. An alternative technique,[58] considers the making of the additional slab using a high performance concrete with a wire mesh: The high mechanical properties of the concrete, combined with the reduced diameter of the net mesh, allow for more reduced thicknesses. Is considered very valid also the use of fibre-reinforced concrete, in which the fibres contained in the strengthening material completely replace the electrowelded net mesh, allowing to have more reduced thickness diaphragms, since it is no longer necessary the addition of any concrete cover. This operation includes the specific improvements of reinforced concrete diaphragms, such as: efficient structural behaviour, reduced costs and ease of implementation with the added advantage of limitation of the increase of the masses and therefore of the seismic stresses. In summary, the improvements of the strengthening of floors with cooperating hood in HPFRC material are the followings: [58]
Alberto Meda and Paolo Riva. “Strengthening of Wooden Floors with High Performance Concrete Slabs”.
In: Restoration of Buildings and Monuments (Formerly: Internationale Zeitschrift für Bauinstandsetzen und Baudenkmalpflege; International Journal for Restoration). Vol. 7. Jan. 2001, pp. 621–640. doi: 10.1515/rbm-20015614.
84
Index > 4 Applications > 4.3 Applying the strengthening technique • Limited thicknesses (20-30 mm); • Low load increase; • No need for reinforcement net mesh; • Increased bearing capacity of the floor associated with the decrease of the displacement of the deck; • Increased stiffness and strength of the compound section with advantageous development of behaviour in bending; • Speedy application because of the self-compacting capacity of the material; • Containment of the variation of the quota of the existing floor; • Regarding seismic adaptation, the decrease in the thickness of the hood causes a limitation of the mass increase, ensuring in any case the diaphragm effect for the distribution of horizontal actions on vertical elements; 4.3.1.2.1
Applicability on RC floors The realization of the strengthening of RC floors with
cooperating hood casting is carried out by preparing the support through scarification up to a suitable depth to remove deteriorated parts and to have a sufficient degree of surface roughness. If it is not possible to perform an adequate scarification, it is suggested to drill holes every 50x50 cm, diameter 22-24 mm and depth 3-4 cm, inside which are inserted metal connectors glued with epoxy resin. Alternatively it is possible to make collaborative roots through pouring. After these operations the support is aspirated. For the structural connection between the strengthening slab and perimeter walls, it is necessary to prepare holes for the parking of the reinforcing bars, cleaning the holes and anchoring the bars with resin. The casting of the fibre-reinforced material is carried out by pouring and then the spreading with straightedge and the positioning of reinforcing bars for the cast restarting is done. In the end, anti-evaporation material based on synthetic waxes or water is sprayed. Alternatively, it is possible to use PE sheets.
4.3.1.3
Strengthening of wooden floors
Lately several solutions have been presented for the consolidation of wooden floors such as: the stiffening with a wooden plank placed orthogonally to the existing boarding panel and nailed it, the 85
Index > 4 Applications > 4.3 Applying the strengthening technique addition of external structural elements, such as steel strengthening beams, the use of collaborating slender concrete slabs. It emerges to be undoubtedly a moderately invasive operation the overlap of a new boarding panel perpendicular to the existing one, since it considers the use of materials totally compatible with the materials of the elements to be strengthened.
The strengthening by the use of metal beams, even if it improves the static properties of the building, could imply a significant increase in the thickness of the floor and generally is adopted in cases where there are no type historical or architectural constraints.
To bypass the constraints of strengthening solutions with wood, such as the insufficient increase in stiffness, and with steel beams, problematic for the aesthetic aspect, it is plausible to think of a technique that considers the casting of a concrete hood with a electrowelded net, cast over the old site and unified with the latter by appropriate connectors, in order to obtain a mixed section in wood-concrete with appreciable increase of inertia of the section itself and therefore also its stiffness (Figure 4.3). The connections may be punctual, such as screws, nails or plugs, or may be diffused as plates or notches.
Concrete hood
Boarding panels
Wooden beam
Peg connectors
Figure 4.3: Diagram of strengthening of floor slabs with concrete[58]
It should be underlined that the more effective the connection used is, the greater the stiffness of the mixed section will be. In order to make the collaboration between wood and concrete, different conjunction types are presented in literature. Among the techniques currently in development, an extensively in-depth solution is one in which the connection between wood and concrete is made 86
Index > 4 Applications > 4.3 Applying the strengthening technique through the insertion of pegs[59][60] ,[61] in other words smooth steel rods inserted in the wood in calibrated holes. The deformability of the conjunction considerably affects the strength and especially the rigidity of the wood-concrete beams. The concept of infinitely rigid connection and flat sections, often embraced by designers, does not appear to be very valid for the verification of the mixed section in cases where appropriate perfecting coefficients are not adopted for a more precise calculation of the stiffness and of the connection strength.
concrete floor
pavement
connector
boarding panel connector
wooden beam
wooden beam
(a) floor and beam in direct contact
(b) passing boarding panel
Figure 4.4: Typical section of an wooden floor made rigid using concrete[59][60] This connection solution is made in these ways:
1. It is removed a planking band at the beams of the deck to allow the concrete to come into contact with the latter and make ribs of a thickness equal to that of the boarding panel in the collaborating slab. In this case the peg connectors appear stressed ideally only in shear and may have small diameters, since the rigidity is moderate. 2. The collaborative slab is cast without the removal of the boarding panel that is crossed by [59]
Piero Gelfi and Alessandra Marini. “Solai misti legno calcestruzzo: metodi di verifica (Prima parte)”. Italian. In:
(153 2008). Ed. by De Lettera Editore, pp. 44–51. issn: 1593-3970. [60] Piero Gelfi and Alessandra Marini. “Solai misti legno calcestruzzo: metodi di verifica (Seconda parte)”. Italian. In: (154 2008). Ed. by De Lettera Editore, pp. 26–31. issn: 1593-3970. [61] Piero Gelfi, Ezio Giuriani, and Alessandra Marini. “Stud Shear Connection Design for Composite Concrete Slab and Wood Beams”. In: ASCE Journal of Structural Engineering 128 (Dec. 2002), pp. 1544–1550. issn: 0733-9445. doi: 10.1061/(ASCE)0733-9445(2002)128:12(1544).
87
Index > 4 Applications > 4.3 Applying the strengthening technique the pegs. The pegs are therefore stressed both in shear and bending and therefore require a higher stiffness than that of the previous case. The connection with bearing vertical elements is realized through the electrowelded net mesh participating in the concrete hood, which generally bonds to curbs inserted into the walls through appropriate additional reinforcements. In summary, these are the improvements of strengthening with cooperating hood: • Increase of stiffness that the concrete hood gives to the entire horizontal structure, excluding big modifications both about the aesthetic aspect and the static one of the pre-existing structure, because the wood participates in the resistant section through the connectors. In addition the concrete casting is carried out directly on the old boarding panel thus not altering the extrados of the ceiling; • Opportunities to implement the strengthening of the deck avoiding having to decrease the height of the inter-plane. Actually the concrete slabs are made of a moderate thickness, usually about 5÷6 cm for lights of 4÷5 m; • Optimization of the entire floor’s plate like behaviour. The insertion of the electrowelded net mesh allows further to connect the horizontal element to the vertical walls making the resistance of the whole building more favourable to seismic stresses; • Greater fire protection unlike techniques that consider the insertion of steel elements; • Economic convenience of the operation that does not require specialized labourers since the intervention of placement of the conjunctions and the casting of concrete are substantially trivial. In recent years a wooden floors strengthening solution has been made feasible, considering the use of a high-performance concrete hood (HPC) of moderate thickness (20 mm), connected to the wooden beam through peg connections.[62] The results of experimental tests have confirmed the validity of this operation in the advantageous refinement concerning static loads as well as for loads in the plane of the deck. The essential benefit of the use of high performance concrete rather than traditional concrete lies in the moderate [62]
Alberto Meda and Paolo Riva. “Consolidamento di solai in legno mediante calcestruzzo ad alte prestazioni”.
Italian. In: Atti del IV Workshop Italiano sulle strutture composte. Jan. 2000.
88
Index > 4 Applications > 4.3 Applying the strengthening technique thickness used in the realization of the strengthening hood, allowing to limit the increase in mass and thickness of the deck, guaranteeing in any case an effective diaphragm effect, as well as being an operation more compatible with traditional materials, less invasive and reversible compared to other commonly used solutions. From a comparison of numerical simulation between the behaviour of wooden diaphragms strengthening with slabs in RC and the behaviour of slabs in FRC[63] it appears that both solutions are effective in preventing a fragile collapse by favouring a ductile failure associated with the yield of the reinforcement of the curbs. This result shows that the fibres are able to completely replace the traditional reinforcement net meshes. Nonetheless, while for the traditional reinforced concrete technique the cracking is immediately followed by the yield of the reinforcement of the curbs, in the solutions in fibre-reinforced concrete the post-peak behaviour appears definitely more stable with progressively softening behaviour, due to the sewing effect exerted by the fibres. For lower seismicity levels, a 2 cm thick, fibre-reinforced concrete diaphragm shows better behavior than a 5 cm RC base diaphragm. In relation to the high level of seismicity, to equalize performance, the diaphragms in fibre-reinforced concrete can have a thickness equal to 3 or 2 cm depending on the fibre content, while for even higher seismicity level, a minimum thickness of 4 cm is required. To conclude, in areas with low and medium level of seismicity, the strengthening with fibrereinforced concrete floor can be more efficient than the ordinary RC hood, precisely because of the possibility of using very small thicknesses with the benefit of a significant reduction in the increase of static loads. In relation to a very high degree of seismicity, the use of fibre-reinforced concrete is still a practicable technique, but the thickness of the slab could not be greatly reduced. Alternatively, it is possible to use a higher degree of fibre content or to increase the strength of the matrix, using High-Performance FRC (HPFRC). Summarizing, these are the advantages of strengthening with collaborating hood in fibrereinforced concrete: • Opportunities to significantly decrease the thickness of the diaphragm, limiting the increase of static loads and seismic actions; • Ease and speed of operation: the replacement of the traditional reinforcement net mesh with [63]
Alessandra Marini, Giovanni Plizzari, and Cristina Zanotti. “Seismic Enhancement of Existing Buildings by
Means of Fiber Reinforced Concrete Diaphragms”. In: Journal of Civil Engineering and Architecture 4 (2009). doi: 10.1061/41084(364)127. url: https://ascelibrary.org/doi/abs/10.1061/41084(364)127.
89
Index > 4 Applications > 4.3 Applying the strengthening technique steel fibres eliminates some drawbacks of the realization with traditional reinforced concrete, linked to the positioning of the net mesh and the need to guarantee a minimum concrete cover;
• Possibility to eliminate or delay the fragile collapse by shear, assuring ductile mechanisms, by appropriate choice of the quantity of fibres;
• Efficient technique for seismic adaptation of both constructions in masonry and RC structures.
4.3.1.3.1
Applicability on wooden floors In similar way to the strengthening of RC floors can
be carried out the strengthening with a collaborative hood in high performance fibre-reinforced concrete of wooden floors. Before casting the hood metallic connectors with screws are placed for the concrete-to-boarding panel connection. After that the waterproof and transpirant sheet is placed to protect the wooden floor and the reinforcing bars are placed for the connection with the bearing structures or the walls. Finally, the hood is cast and spread with straightedge.
4.3.1.3.2
Strengthening at bending The floor diaphragms with cast collaborating FRC slabs
increase the rigidity of the floor and its strength against the static loads and the horizontal actions caused by the earthquakes, this still with limited thickness of the slab. In situations of strengthening for flexure it may be necessary to position connectors between the strengthening material and the initial concrete. In shear strengthening situations the connectors are essential. In the situations of construction of diaphragms of deck, it is necessary to foresee also connectors of connection between the strengthening slab and the perimeter walls.
Unstrengthened floor It is taken into consideration the concrete-and-masonry floor with reinforced concrete beams in Figure 4.5[64] . For both the initial concrete and the reinforcing steel bars it is considered an FC confidence factor equal to 1.2. [64]
Alberto Meda. “Dispense: Rinforzo con incamiciatura in HPFRC (Seconda Parte)”. Italian. In: (Feb. 2011).
Rinforzo di solai per l’adeguamento sismico: Rinforzo di solai in CA. url: http : / / www . ordineingegneri . bergamo.it/wp/wp-content/uploads/2013/06/Dispense-21.2.2011-Prof.-Meda-seconda-parte-.pdf.
90
Index > 4 Applications > 4.3 Applying the strengthening technique B t
h'
d
h As
b
Figure 4.5: Cross-section of the concrete floor beam to be strengthened[64]
4.3.1.3.3
Floor strengthened with FRC hood
It is intended to consolidate the previous floor
with casting of a collaborating FRC hood of thickness equal to 30 mm. See Figure 4.6. B hrinf t
h'
d
h As
b
Figure 4.6: Cross-section of the beam strengthened with HPFRC[64]
Floor strengthened with FRC hood on polystyrene sheets If it is wanted to obtain an increase in stiffness, a contained thickness of FRC material can be used, however, by introducing between this and the initial structure a layer of EPS or similar material for weight lightening. For example, the previous floor is strengthened by casting a collaborating hood in FRC material with a thickness of 30 mm, with insertion of polystyrene elements of thickness 40 mm as shown in Figure 4.7. 91
Index > 4 Applications > 4.3 Applying the strengthening technique B hrinf hpol t
h'
d
h As
b
Figure 4.7: Cross-section of the beam strengthened with HPFRC and polystyrene sheets[64]
4.3.2
Beam strengthening
Apart from the known problems of seismic optimisation, the strengthening of reinforced concrete buildings may also appear necessary because of the deterioration of the materials or the increase of the loads compared to those of the design. Load [kN]
Load [kN]
400
500 400
300
300 200
200 100
100
Displacement [mm]
0 0
20
40
60
SLS
Displacement [mm]
0 0
80
4
8
12
16
20
(b)
(a)
Figure 4.8: Comparison of load-displacement curves of strengthened beams: (a) full curves; (b) initial part of the curves (for the Serviceability Limit State)[65]
The opportunity to use high-performance FRC concretes (HPFRC) for the strengthening of beams was at the base of contemporary researches with goal the increase of the flexural capacity 92
Index > 4 Applications > 4.3 Applying the strengthening technique of the structural elements.[65] Through experimental bending tests on strengthened beams with high performance fibrereinforced concrete jacketing, the validity of this solution has been proved in the increase in flexural capacity in cases of strengthening as well as in cases of restoration or repairing of previously damaged beams. In Figure 4.8 is shown the comparison diagrams of the load-displacement at midspan relations of tests performed on beams. From the diagrams it is perceived that the application of a 40 mm thick jacket allows to reach an increase of the bearing capacity with un ultimate load equal to 2.15 times that of the unstrengthened beam, despite the post-peak behaviour shows a degradation. However, already at the end of the downhill branch, the load is consolidated with a tendency to large horizontal lines on a value greater than the ultimate load of the unstrengthened corresponding specimen. It is further appropriate to emphasize the fact that the maximum load of the jacket strengthened beam and without longitudinal reinforcement bars is higher than that achieved by the unstrengthened reinforced beam.
(a)
(b)
(c)
Figure 4.9: Beam crack pattern at failure: (a) Beam in reinforced concrete without HPFRC jacket; (b) Not reinforced beam, with HPFRC strengthening jacket; (c) RC beam with HPFRC jacket[65] Regarding ductility, in the strengthened beams there is a decrease in the ultimate displacement, [65]
Giovanni Martinola, Alberto Meda, Giovanni Plizzari, and Zila Rinaldi. “Strengthening and repair of RC
beams with fiber reinforced concrete”. In: Cement & Concrete Composites 32 (Oct. 2010), pp. 731–739. doi: 10.1016/j.cemconcomp.2010.07.001.
93
Index > 4 Applications > 4.3 Applying the strengthening technique even if the high ductility of the unstrengthened beam is in truth apparent and related, partially, to the loss of adherence between reinforcement bars and concrete. In any case, in the circumstances in which an increase of ductility is required, it is possible to consider to insert a net mesh inside the casting of the jacket. A further important aspect of the in-depth solution concerns serviceability situations. In fact, the current norms require to verify the strengthening of the structure both to the ultimate limit state, that is the increase of the flexural capacity, and to the serviceability limit state, i.e. the control of the deformations and the crack opening. Seen from this point of view, the solution offered allows to significantly optimize the operating behaviour, significantly decreasing the displacement in mid-span. The jacket behaves like a kind of confinement used from the outside, postponing in time the transit from the initial rigidity of the not cracked beam to that, far lower, of the partialised section, preventing the development of macro-cracks with evident benefit from the point of view of stiffness and durability, due also to the very low ratio of water/cement of the strengthening matrix. At the same serviceability load, the cracking framework of the unstrengthened beam is fully developed, as shown in Figure 4.9.
Load [kN]
Load [kN] 500
500
Strengthened Repaired
400
400
300
300
200
200
100
100
Displacement [mm]
0 0
20
40
60
80
Strengthened Repaired
Displacement [mm]
0 0
4
8
12
16
20
24
28
32
(b)
(a)
Figure 4.10: Comparison of the load-displacement results for beams strengthened with HPFRC jacket: (a) At Ultimate Limit State; (b) At Serviceability Limit State.[65]
Experimental tests were also performed to estimate the validity of this solution for repairing damaged beams. In Figure 4.10 is shown the comparison of the load-displacement curves in mid-span relations of a high-performance fibre-reinforced concrete beam and a similar beam subject to a preventive test till the yield of the reinforcing bars, then the repair is carried out by casting of the jacket, and 94
Index > 4 Applications > 4.3 Applying the strengthening technique at the end is tested again. The results demonstrate for the repaired beam a similar behaviour to that of the strengthened beam, with a slightly lower initial stiffness. The bearing capacity results 1.9 times that of the unstrengthened solution, a slightly lower value if compared to the example of the corresponding strengthened beam because of the existence of cracks in the damaged beam which are not repaired before the casting of the jacket. The collapse mechanism, the cracking framework and the post-peak behaviour are comparable to those seen in the consolidated beam. Regarding SLS, the proposed technique also allows a significant increase in stiffness with a displacement 12 times lower than that of the unstrengthened beam.
Figure 4.11: Loading frame[66]
Equally important is the need to increase the capacity of RC elements towards shear actions, since the existing building heritage is often characterized by structure with inadequate or insufficient shear reinforcement. 95
Index > 4 Applications > 4.3 Applying the strengthening technique In Figure 4.11[66] is shown the loading frame used from Mostosi, Riva, Maringoni, and Meda (2011) in carrying out the tests.[67] Lately a campaign of experimental tests has been completed on the analysis of the validity of the technique for increasing the shear capacity of beams by using HPFRC jacketing.[68][69][70][71][72] Results of experimental bending tests have shown the contribution of the HPFRC jacket in the definition of the mechanism of collapse, in the influence on the post-peak behaviour and the formation and evolution of the cracking framework. Differently from the reference beam without reinforcement bars, which suffers a shear failure, the beams with HPFRC jacketing reached a flexure failure, with a reduced influence of the effects of the shear stresses. The jacket in fact works in an analogous manner to a shear reinforcement and is, therefore able to replace it completely. It is of remarkable interest to highlight the fact that the beams strengthened respectively with jacket cast completely with pourable fibre-reinforced high performance concrete or with cast caseback in pourable fibre-reinforced high performance concrete and lateral bands implemented with [66]
Stefano Maringoni, Serena Mostosi, Alberto Meda, and Paolo Riva. “Rinforzo a taglio di travi in C.A. mediante
incamiciature in calcestruzzo ad elevate prestazioni”. Italian. In: Atti del 26° Convegno Nazionale AICAP 2011: Lo sviluppo delle opere in c.a. nel terzo millennio, Padova, Italia 19 - 21 maggio 2011. AICAP - Associazione Italiana Calcestruzzo Armato e Precompresso. 2011. [67] Serena Mostosi, Paolo Riva, Stefano Maringoni, and Alberto Meda. “Shear strengthening of RC beams with high performance jacket”. In: Proceedings of the fib Symposium 2011: Concrete engineering for excellence and efficiency, Prague, Czech Republic, 8 - 10 June 2011. International Federation for Structural Concrete (fib). Jan. 2011. isbn: 978-80-87158-29-6. [68] Alberto Meda, Serena Mostosi, and Paolo Riva. “Strengthening of RC Beams with High Performance Jackets”. In: Studies and Researches - Annual Review of Structural Concrete 31 (2011-2012). Ed. by Starrylink. issn: 11216069. [69] Alberto Meda, Serena Mostosi, and Paolo Riva. “An application of high performance jacketing for the shear strengthening of RC beams”. In: Proceedings of the 4th CTE International Symposium: Advances in cementitious materials and structure design, Brescia, Italy, 17th-20th June 2012. Ed. by CTE. University of Brescia. 2013. [70] Stefano Maringoni, Serena Mostosi, Alberto Meda, and Paolo Riva. “Strengthening of R/C members by means of high performance concrete”. In: Proceedings of the 12th International Conference on Recent Advances in Concrete Technology and Sustainability Issues, Prague, Czech Republic, 31st October - 2nd November 2012. Ed. by Terence C. Holland, Pawan R. Gupta, and V. M. Malhotra. ACI SP 289. International Federation for Structural Concrete (fib). Prague, Czech Republic: American Concrete Institute (ACI), 2012, pp. 201–214. isbn: 978-1-62276-641-3. [71] Serena Mostosi, Alberto Meda, Paolo Riva, and Stefano Maringoni. “Strengthening of R/C beams with high performance concrete jacket”. In: Proceedings of the 8th RILEM International Symposium on Fiber Reinforced Concrete: challenges and opportunities (BEFIB 2012). Ed. by Joaquim A.O. Barros. RILEM. Guimarães, Portugal: RILEM Publications SARL, Jan. 2012. isbn: 978-80-87158-29-6. [72] Alberto Meda, Serena Mostosi, and Paolo Riva. “Shear Strengthening of Reinforced Concrete Beam with High-Performance Fiber-Reinforced Cementitious Composite Jacketing”. In: ACI Structural Journal 111 (5 2014), pp. 1059–1067.
96
Index > 4 Applications > 4.3 Applying the strengthening technique thixotropic HPFRC present completely comparable behaviours until the maximum load is reached. It is therefore evident how the strengthening in HPFRC allows to increase the bearing capacity in flexural terms, with values enclosed between 1.5 and 1.7 times the strength of the unstrengthened beam. The solution presented, in addition, contributes to an increase of stiffness and, consequently, a decrease of the displacement in mid-span under service before the arrival at the peak. It is pointed out that while for the unstrengthened beam the failure is fragile, for the strengthened beams the post-peak behaviour results more ductile. Summarizing, taking into consideration the results of the experimental tests, these are the improvements of the use of U-jacket in high-performance fibre-reinforced concrete for the strengthening of beams: • Increase in bearing capacity in comparison to techniques originally without reinforcement towards shear, on average of about 1.6 times; • Higher stiffness initially, meaning a lower displacement in mid-span, so a reduction of the deformability under service; • Increase of the shear strength that, resulting higher than the that in flexure, causes a flexural failure mechanism, therefore, ductile with small influence of shear effects; • Operatively simple, especially in cases of use of thixotropic materials, which do not need formworks and makes it so easy to implement even on structural elements of difficult accessibility; • Increase in durability and optimisation of fire and high temperature behaviour. 4.3.2.1
Coupling beams
A case of specific attention from the engineering point of view is represented by the coupling beams in reinforced concrete. In the presence of structural elements characterized by discrete ratios of slenderness, the lack of possibility of using kinematic models of the Euler-Bernoulli type obliges the use of design methods based on ordinary systems of strut/tie. The use of high performance fibre-reinforced materials, distinguished by ductile behaviour in tension, would intuitively suggest important reductions in the ordinary reinforcing bars. However, it is essential to highlight 97
Index > 4 Applications > 4.3 Applying the strengthening technique how the strong lack of symmetry in mechanical performance, compression and tension can be of origin to fragile mechanisms at specific levels, particularly in cases of concentrated actions. This experimental evidence is captured during a series of experimental tests on prismatic specimens exposed to stress states at the neck of bottle bottle.[73] The stocky elements generally intended for the connection of the walls constituting the braced nuclei exhibit non-rare criticalities related to moderate reinforcement levels and inadequate constructive solutions. From this point of view, high performance FRC composites represent a valid technique for the adaptation or renovation of existing constructions[74] .[75]
4.3.2.2
Applicability on beams
The casting of the jacket for the strengthening of beams is performed on the sides and near the extrados surface. It can be in pourable or thixotropic HPFRC material. If the material is pourable, perfect sealing formworks are necessary and the execution of the casting is done from above. If the material is thixotropic concrete, a formwork is mounted on the top of the beam for the casting of the lower layer in pourable HPFRC, while for the lateral surfaces is considered the application of thixotropic material using trowel. It is suggested, before the application of the strengthening material, the laying of a layer of epoxy primer on the surface of the beam. At the beginning of the operation it is necessary to prepare the support by sandblasting or scarification and hydrowashing. Also in this case is possible to consider the placement of a [73]
Matteo Colombo and Marco Di Prisco. “D-Zones in HPFRC”. in: High Performance Fiber Reinforced Cement
Composites 6: HPFRCC 6. Ed. by Antoine E. Naaman, Gustavo J. Parra-Montesinos, and Hans W. Reinhardt. 1st ed. Vol. 2. RILEM Bookseries. Springer Netherlands, 2012, pp. 205–212. isbn: 978-94-007-2435-8. doi: 10.1007/978-94-007-2436-5. [74] Matteo Colombo, Marco Di Prisco, and Anna Magri. “TRM and UHPFRC: Retrofitting solutions for structural elements”. In: Proceedings of the 3rd International Conference on Concrete Repair, Rehabilitation and Retrofitting, ICCRRR-3, 3-5 September 2012, Cape Town, South Africa. Cape Town, South Africa: CRC Press - Taylor and Francis Group, Sept. 2012, pp. 460–461. isbn: 978-0-415-89952-9. [75] Milot Muhaxheri, Alessandro Spini, Liberato Ferrara, Marco Di Prisco, and Marco G. L. Lamperti Tornaghi. “Strengthening/retrofitting of coupling beams using advanced cement based materials”. In: Proceedings of the 4th International Conference on Concrete Repair, Rehabilitation and Retrofitting, ICCRRR-4, 5-7 October 2015, Leipzig, Germany. Ed. by Frank Dehn, Hans-Dieter Beushausen, Mark G. Alexander, and Pilate Moyo. Leipzig, Germany: CRC Press - Taylor and Francis Group, 2015, pp. 733–741. isbn: 978-1-138-02843-2.
98
Index > 4 Applications > 4.3 Applying the strengthening technique electrowelded net mesh U-shaped. It may be advisable, in order to guarantee the anchoring of the jacket, to prepare the concrete casting restart bars inside the slab. When the concrete of the cover is very damaged, before the casting of the jacket is necessary to remove the cover, clean the support and to provide for the protection of the reinforcement bars using passivating products. 4.3.2.3
Design strength in bending
In this paragraph are described the procedures for the calculation of the design strength in bending of beams strengthened with U-jacket in FRC material. Regarding the bending strength, three methods are indicated: 1. A rigorous, accurate, but certainly more laborious method; 2. An approximate method, very fast but also much less precise; 3. A simplified procedure for verifying at ULS, a compromise between the previous methods’ difficulty and accuracy. 4.3.2.3.1
Rigorous method: moment-curvature diagram The rigorous procedure considers
the development of a method capable of approximating with sufficient accuracy the nonlinear behaviour of strengthened sections in FRC material and of defining a diagram of bending moment and curvature by estimation of various relevant points. This method focuses on the solution of equilibrium and congruence equations in a iterative way. For each point of the moment-curvature curve, are evaluated the deformations, the position of the neutral axis, the stresses in the materials and the value of the corresponding bending moment. The failure of the beam is determined as the reaching of the ultimate deformation in tension of the FRC or of the steel, in compression of the base concrete or of the FRC material. Constitutive laws of the materials The initial step of the method foresees the schematization of the constitutive bonds of the materials, through the integration by adopting simplifications to represent the real behaviour as faithfully as possible. 4.3.2.3.2
Simplified method: Evaluation of the ultimate moment The rigorous procedure
described can be used when precise values are wanted regarding the ductility of the section. This procedure would be laborious for a verification of the resistant moment. It is therefore proposed a simplified procedure with different limits regarding a further simplification of the constitutive bonds, but which allows to calculate the resistance of a strengthened section with a good approximation. 99
Index > 4 Applications > 4.3 Applying the strengthening technique Hypotheses The traditional approach is followed at ULS governed by the current norm. The following hypotheses are used: 1. Navier-Bernoulli hypothesis, the sections rotate remaining flat; 2. Negligible strength in tension for traditional concrete; 3. Perfect adherence between concrete-reinforcing steel bars; 4. Parabolic-rectangle diagram for compressed concrete using the stress-block representation; 5. Elasto-plastic relation for reinforcing steel bars in tension and compression. The same hypotheses are used for the FRC material in compression. Regarding the deformation values for the determination of the stress-block, two cases are considered: • Class lower than C50/60: εF cu = 3.5‰; εF c4 = 0.7‰ fc k ) 4 • Class higher than C50/60: εF cu = 2.6‰+ 35‰·[ (90− 100 ] ; εF c4 = 0.2εF cu
A constant stress distribution is used in tension for the FRC material. The failure of the beam is determined as the reaching of the ultimate tensile deformation of the FRC material or of the steel, in compression of the ordinary concrete or of the FRC material. Evaluation of the design resistant moment
For the evaluation of the design resistant mo-
ment, the distribution of deformations and of the stresses is shown in Figure 4.12. In the detailed expression, the contributions of the HPFRC jacket material of the lower layer and of the two lateral layers are evaluated in a separate way in order to allow the extension of the formulation also to the use cases of two different types of strengthening. The position of the neutral axis is deduced from equilibrium to horizontal translation: fcd · b · αcc · x + fF cd, L · 2 · s L · αF c · x + σsc · Asc + − fFt d, L · 2 · s L · (h − x) − fFt d, I · sI · (b + 2 · s L ) − σst · Ast = 0
Equation 4.3[64]
It is evaluated the resistant moment from equilibrium to rotation: αc 2 αF c MRd = fcd · b · αcc · 1 − · x + fF cd, L · 2 · s L · αF c · 1 − + 2 2 (h − x)2 + σsc · ASc · (x − c) + fFt d, L · 2 · s L · + 2 sI + fFt d,I · sI · (b + 2 · s L ) · h − x + + σst · ASt · (d − x) 2
Equation 4.4[64]
Initially it is hypothesized to arrive at the ultimate deformation in the compressed concrete at the top edge, with failure of the fibre-reinforced concrete. Should be noted that when the FRC 100
Index > 4 Applications > 4.3 Applying the strengthening technique material is of class lower than C50/60, the ultimate deformation is equal to the 3.5 ‰, equal to that of the concrete of the nucleus. So there is simultaneous failure of both of the two concretes; When the FRC material is of class higher than C50/60, its ultimate deformation will be smaller than that of the nucleus concrete. Therefore the failure will be on the FRC side. nucleus concrete
f Fcd,L
f cd
x
αFcx
Asc
Ascσsc
α cx
εcc = εFc,L ε sc
c
HPFRC
f Ftd,L d
h
Ast
ε st εFt,L
SI SL
f cd
b
SL
Astσst
εFt,I
f Ftd,I
Compressive design strength of traditional concrete
f Fcd,L Compressive design strength of HPFRC on the sides f Ftd,L Tensile design strength of HPFRC on the sides
f Ftd,I
Tensile design strength of HPFRC of the caseback
σsc
Stress on the upper bars
σst
Stress on the lower bars
Figure 4.12: Strengthened section: stress and strain diagrams[64] It is imposed εcc = εF c, L = εF cu . The factors αcc and αF c express, if a stress-block type schematization is adopted, the percentage of the neutral axis on which the uniform distribution of the compression stresses of concrete and FRC act. These coefficients are described by these expressions: • αcc =
εc c −εc4 εc c
• αF c =
ε F c −ε F c4 εF c
Before estimating the resistant moment, it is necessary to carry out the control on the deformations to determine if the reinforcement bars are elastic or yielded and if at the tensed part has been exceeded the maximum deformation in the FRC. This may involve a new calculation of the neutral axis according to a iterative procedure. Alternatively, the deformations of the various materials are described according to the ultimate deformation of the FRC in compression, the evaluation of the 101
Index > 4 Applications > 4.3 Applying the strengthening technique associated stresses is performed, the expressions are inserted in Equation 4.3[64] and is evaluated the neutral axis in only one step by resolving the second degree expression. It is proceeded with the following steps. Step 1: Control of the tensed reinforcement bars It is described the deformation of the tensed reinforcement bars εst as a function of the deformation of the compressed FRC εF c and it is compared with the deformation of the steel at the elastic limit εst,el : εst =
εF c, L · (d − x) x
Equation 4.5[64]
with: fyd,t Es is the design yield strength of the tensed reinforcement bars. εst,el =
where fyd,t
Equation 4.6[64]
If εst > εst,el then the reinforcement bars are yielded; εst < εst,el then the reinforcement bars are in elastic field; The term σst · Ast in Equation 4.3[64] is replaced with the following expressions: σst · Ast Yielded
Elastic Es · ε F c ·
fyd,t · Ast
(d−x) x
· Ast
Table 4.2: [The substitution of the term σst · Ast [64] Step 2: Control of the compressed reinforcement bars It is described the deformation in the compressed reinforcement bars εsc as a function of the deformation of the compressed FRC εF c and it is compared with the deformation of the steel at the elastic limit εsc,el : εsc =
εF c, L · (x − c) x
Equation 4.7[64]
with: fyd,c Equation 4.8[64] Es is the design yield strength of the compressed reinforcement bars. If εsc > εsc,el εsc,el =
where fyd,c
then the reinforcement bars are yielded. If εsc < εsc,el then the reinforcement bars are in elastic field. The term σsc · Asc in Equation 4.3[64] is replaced with these expressions: 102
Index > 4 Applications > 4.3 Applying the strengthening technique σsc · Asc Yielded
Elastic Es · ε F c ·
fyd,c · Asc
(x−c) x
· Asc
Table 4.3: The substitution of the term σsc · Asc [64]
Step 3: Control of the tensed FRC
It is described the deformation in the tensed FRC of the
caseback εFt,I as a function of the deformation of the compressed FRC εF c and it is compared with the conventional value assumed for the ultimate deformation varepsilonFTU : εFt, I =
εF c, L · (h + sI − x) x
Equation 4.9[64]
If εFt,I < εFt,u then it is proceeded with calculation of the resistant moment according to the Equation 4.4[64] . If εFt, I > εFt,u then it is necessary to start afresh by imposing the tensile failure of the FRC of the caseback. It is supposed at the tensed edge the failure on the side of the FRC of the caseback, so the deformation εFt, I is equal to the ultimate tensile deformation. It is imposed εFt,I = εFtu . As in the previous situation, before continuing with the evaluation of the resistant moment, it is needed perform a check on the deformations to see if the reinforcement bars are elastic or yielded. This may mean a new calculation of the neutral axis with the a iterative procedure. Alternatively, deformations of the different materials are described as a function of the ultimate tensile deformation of the FRC of the lower layer, the associated stresses are evaluated, the expressions are replaced in the Equation 4.3[64] and it is found the neutral axis in a single step by resolving the second degree expression. At the end the deformations at the upper edge are determined in the compressed concrete and FRC material. So the following steps are followed.
Step 1: Control of the tensed reinforcement bars
It is described the deformation in the
tensed reinforcement bars εst as a function of the deformation of the tensed FRC of the caseback εFt, I and it is compared with the deformation of the steel at the elastic limit εst,el : εst =
εFt,I · (d − x) (h + sI − x)
Equation 4.10[64]
If εst > εst,el then the reinforcement bars are yielded. If εst < εst,el then reinforcement bars are in elastic field. The term σst · Ast in Equation 4.3[64] is replaced with these expressions: 103
Index > 4 Applications > 4.3 Applying the strengthening technique σst · Ast Yielded fyd,t · Ast
Elastic Es · εFt, I ·
(d−x) (h+s I −x)
· Ast
Table 4.4: The substitution of the term σst · Ast with expressions[64]
Step 2: Control of the compressed reinforcement bars It is described the deformation in compressed reinforcement bars εsc as a function of the deformation of the tensed FRC of the caseback εFt, I and it is compared with the deformation of the steel at the elastic limit εsc,el : εsc =
εFt, I · (x − c) (h + sI − x)
Equation 4.11[64]
If εsc > εsc,el then the reinforcement bars are yielded. If εsc < εsc,el then the reinforcement bars are in the elastic field. The term σsc · Asc in Equation 4.3[64] is replaced with expressions: σsc · Asc Yielded fyd,c · Asc
Elastic Es · εFt, I ·
(x−c) (h+s I −x)
· Asc
Table 4.5: The substitution of the term σsc · Asc with expressions[64]
Step 3: Control of the deformation of the compressed concrete and FRC It is described the deformation in the concrete εcc and in the FRC εF c, L compressed at the top edge as a function of the deformation of the tensed FRC εFt,I for the calculation of the factors αcc and αF c . εcc = εF c, L ·
εFt, I · x (h + sI − x)
Equation 4.12[64]
By substituting the specified quantities in the Equation 4.3[64] , it is found the position of the neutral axis by resolving the second degree expression and determining the value of the resistant moment with Equation 4.4[64] . 4.3.2.3.3
Approximate method For a more immediate calculation in the design phase of the
flexural strength of the strengthened section, it is considered an approximate method, less laborious than the previous one, based only on the equilibrium equations. This method can be used for presizing for the design of the strengthening operation. As the method does not foresee any control over the deformations, it is necessary to carry out that control during the verification phase using 104
Index > 4 Applications > 4.3 Applying the strengthening technique the rigorous procedure described in Paragraph 4.3.2.3.1 or the simplified method explained in Paragraph 4.3.2.3.2. Hypotheses For the laws are used the same schematizations of the simplified method, therefore, the traditional approach to the ultimate limit state governed by the norms in force, with the use of the stress-block for both materials, for the concrete and for FRC material in compression and a constant stress distribution for the FRC material in tension with the evaluation of the tensile equivalent strength fFt,eq based on the equivalence of the moment. Evaluation of the design resistant moment
For the evaluation of the design resistant mo-
ment, reference is made to the distribution of the deformations and of the stresses shown in Figure 4.13. It is supposed a failure crisis on the compressed concrete side at the upper edge, thus both materials reach the ultimate deformation εcc = εF c, L , considered equal to 3.5‰and is assumed that the upper and lower reinforcement bar are yielded. nucleus concrete εcc = εFc,L= 3.5‰ ε sc
f cd
Ascf yd,c
x
0.8x
c
Asc
HPFRC f Fcd,L
f Ftd,L d
h
Ast
ε st εFt,L
SI SL
b
SL
Astf yd,t
εFt,I
f Ftd,I
Compressive design strength of traditional concrete
f Ftd,I
Tensile design strength of HPFRC of the caseback
f Fcd,L Compressive design strength of HPFRC on the sides
f yd,c
Yield design strenth of the upper bars
f Ftd,L Tensile design strength of HPFRC on the sides
f yd,t
Yield design strenth of the lower bars
f cd
Figure 4.13: Strengthened section: stress and strain diagrams (approximate method)[64]
No control is performed on the actual state of yielding of the reinforcement bars, neither on the possibility that the upper reinforcement bars be tensed rather than compressed. No control is 105
Index > 4 Applications > 4.3 Applying the strengthening technique performed on the tensile strain in the FRC material. From equilibrium to horizontal translation, the position of the neutral axis is obtained: fcd · b · 0.8 · x + fF cd, L · 2 · s L · 0.8 · x + fyd,c · Asc + − fFt d, L · 2 · s L · (h − x) − fFt d,I · sI · (b + 2 · s L ) − fyd,t · ASt = 0
Equation 4.13[64]
From equilibrium to rotation it is estimated the resistant moment: MRd = fcd · b · 0.8 · 0.6 · x 2 + fF cd, L · 2 · s L · 0.8 · 0.6 · x 2 + (h − x)2 + + fyd,c · ASc · (x − c) + fFt d, L · 2 · s L · 2 sI + fFt d, I · sI · (b + 2 · s L ) · h − x + + 2 + fyd,t · ASt · (d − x) 4.3.2.4
Equation 4.14[64]
Shear design strength
H = 480
d = 410 c = 40
SI = 30
h = 450
A's
As
SL = 30
b = 200
SL = 30
Figure 4.14: Cross-section of the strengthened beam[64] In this paragraph are shown procedures for the calculation of the shear design strength of beams strengthened with U-jacketing in FRC material. The strengthening with HPFRC jacket results valid for weakly shear reinforced beams for which an increase of the shear strength is needed. It is evaluated the contribution of the jacket considering the lateral layers in HPFRC as if they were equivalent stirrups. The following is a method for estimating the shear design strength of strengthened beams with U-shaped jackets in HPFRC (Figure 4.14). 106
Index > 4 Applications > 4.3 Applying the strengthening technique 4.3.2.4.1
Shear strength of the unstrengthened beam For the estimation of the shear strength
of the strengthened beam VRd, N R are used the analytical expressions that are employed to estimate the strength of elements with transverse shear reinforcement stirrups [53] . The shear strength is the lowest value between the strength of the core concrete VRdc and the strength of the transverse reinforcement stirrups VRds : VRd, N R = min (VRds ; VRdc )
Equation 4.15[53]
Regarding transverse reinforcement, the calculation of the shear-tension strength is evaluated as follows: VRds = 0.9 · d ·
Asw · fyd · (ctgα + ctgθ) · sinα s
Equation 4.16[53]
where: d = section’s useful height; Asw = transverse reinforcement area; s = step of the transverse reinforcement stirrups; fyd = tensile design strength of the transverse reinforcement; α = angle of inclination of the transverse reinforcement with respect to the beam. for vertical stirrups α = 90°; θ = inclination of the struts of concrete with respect to the axis of the beam, so that 1 ≤ ctgθ ≤ 2.5. With respect to the concrete of core, the shear-compression design strength is estimated as follows: 0 · VRdc = 0.9 · d · bw · αc · fcd
(ctgα + ctgθ) 1 + ctg2 θ
where bw = section width; αc is an enlarging factor equal to: • 1 for not compressed elements; • 1+
σc p fc d
for 0 ≤ σcp ≤ 0.25 · fcd ;
• 1.25 for 0.25 · fcd ≤ σcp ≤ 0.5 · fcd ; σ • 2.5 · 1 − fccdp for 0.5 · fcd ≤ σcp ≤ fcd ; 0 is the compressive strength of the concrete of core, equal to 0.5 · f 0 ; fcd cd
σcp =
NE d Ac
is the average compression stress in the section (≤ 0.2 · fcd ); 107
Equation 4.17[53]
Index > 4 Applications > 4.3 Applying the strengthening technique 4.3.2.4.2
Shear strength of the strengthened beam The contribution to shear strength of the
strengthening is estimated as: ∆VRd,F = 0.9 · H · 2 · s L · fFt d · ctgθ 0
Equation 4.184.18[64]
where: H = h + sI = total height of the strengthened section; s L = lateral thickness of strengthening; fFt d = tensile design strength for the HPFRC, assumed equal to the maximum tensile strength fFt,max obtained from direct tension tests divided by the coefficient on the material γF ; θ 0 = angle of inclination of the struts of concrete with respect to the axis of the beam in the case of reinforced section, such for which 1 ≤ ctgθ 0 ≤ 2.5. From which the shear strength of the reinforced section is equal to VRd,R = VRd, N R + ∆VRd,F .
4.3.3
Column strengthening
Regarding the strengthening of columns, investigations carried out in recent years demonstrate the validity of the use of a high-performance fibre-reinforced concrete jackets of 40-50 mm thickness in the increase not only of the bearing capacity towards static loads but also of the strength and ductility for what concerns the seismic loads. 4.3.3.1
Increasing capacity towards static loads
As for the increase in capacity towards static loads, the test results of compression-flexure of columns with high-performance fibre-reinforced concrete jackets, subjected to high axial loads, have demonstrated the validity of this solution in offering an effective confinement action, preventing the emergence of symptoms related to the detachment of the concrete cover and the subsequent instabilization of the longitudinal reinforcement bars. The increase in resistance appears strong bearing in mind that the total axial load exerted on the non-reinforced specimen is approximately equal to the compression load at failure of the unstrengthened specimen.[76] The specimen reaches failure for tensile breaking of one of the reinforcing bars corresponding to a drift of 1.7% with limited cracking of the HPFRC jacket at the compressed edges with rare vertical capillary cracks. [76]
Consuelo Beschi, Paolo Riva, Serena Mostosi, and Stefano Maringoni. “HPFRC Jacketing of Perimetral and
Highly Stressed RC Columns”. In: Proceedings of the 9th Rilem International Symposium on Fiber Reinforced Concrete. September 19th - 21st, 2016. Vancouver, Canada: RILEM Publications, Sept. 2016.
108
Index > 4 Applications > 4.3 Applying the strengthening technique 4.3.3.2
Increasing capacity towards seismic loads
The outcomes of experimental tests carried out in recent years demonstrate how the proposed solution is also valid for the increase of the bearing capacity towards the seismic loads.[77][78][79] Hydraulic jacks Axial load application element
Hinges system Horizontal force transfering element
Load cell
Test specimen
Electromechanical jack
Steel foundation connections
Axial load application element
Figure 4.15: Set-up for cyclic loading test[84] Results of experimental investigations have proved that through the application of a highperformance jacket it is feasible to increase the bearing capacity of the columns, compared to similar unstrengthened specimens, with average increases of 60% and 70% in the cases of jacketings on the 4 sides and respectively on the 3 sides (U-jacket) and towards the stress parallel to the [77]
Consuelo Beschi, Stefano Maringoni, Alberto Meda, Paolo Riva, and Francesca Simonelli. “Utilizzo di incami-
ciature in calcestruzzo ad alte prestazioni per il rinforzo di pilastri in un intervento di adeguamento sismico”. Italian. In: 17° Congresso CTE Roma, 5-8 novembre 2008. 2008, pp. 913–920. isbn: 978-88-903647-3-0. [78] Laura Maisto, Alberto Meda, Giovanni Plizzari, and Zila Rinaldi. “Rinforzo di pilastri in ca con incamiciatura in calcestruzzo fibrorinforzato ad elevate prestazioni”. Italian. In: Atti del 17° Congresso CTE Roma, 5-8 novembre 2008. CTE. 2008, pp. 921–928. isbn: 978-88-903647-3-0. [79] Consuelo Beschi, Alberto Meda, and Paolo Riva. “Rinforzo di pilastri con incamiciature ad elevate prestazioni”. Italian. In: Atti del XIII Convegno Nazionale ANIDIS: L’Ingegneria Sismica in Italia. Bologna, Palazzo "Re Enzo" dal 28 giugno al 2 luglio 2009. ANIDIS. 2009. isbn: 978-88-904292-0-0.
109
Index > 4 Applications > 4.3 Applying the strengthening technique main axis of the strengthening.[80]
-10
-8
-6
-4
0
-2
6
4
2
10 [δ/δy]
8
(a)
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7 Drift [%]
200
Horizontal Load [kN]
150 100 50
(b)
0 -50 -100 -150 -200 -140 -120 -100 -80
-60
-40
-20
0
20
40
60
80
100
120
140
Displacement [mm]
Figure 4.16: (a) Load history; (b) Horizontal load versus displacement[80]
In situations where the column is strengthened on the 3 sides (U-shaped) and the stress orientation is transverse to the strengthening axis, the increase in strength appears more limited with [80]
Consuelo Beschi, Alberto Meda, and Paolo Riva. “High Performance Fiber Reinforced Concrete Jacketing in
a Seismic Retrofitting Application”. In: Proceedings of the 2009 ATC & SEI conference on Improving the Seismic Performance of Existing Buildings and Other Structures, San Francisco 9-11/12/2009. Sept. 2009, pp. 224–233. isbn: 978-0-7844-1084-4. doi: https://doi.org/10.1061/41084(364)22.
110
Index > 4 Applications > 4.3 Applying the strengthening technique a maximum load increase of 40% and 10% respectively for positive and negative displacements, higher for positive stress because the jacket works on the compressed side and smaller in situations of negative stresses because the jacket works in tension. The effect in tension is mainly lost for very small drifts this linked to the deformation grouping in a single crack located in the column-foundation connection zone. Even for negative drifts the load of the strengthened columns is shown in every way higher when compared to that of the not jacketed specimen this because of the contribution in compression of the lateral HPFRC layers. Relative to the ductility the solution showed allows to increase the performance of the columns, with ductility 3 times higher for the column jacketed on four sides. For jacket applied on the 3 sides and towards of stress parallel to the axis of the strengthening, the increase in terms of ductility appears less strong but still remains remarkable, with the strengthened specimen reaching a ductility 1.3 times higher compared to the ductility of the unstrengthened specimen. 2 1.8 1.6
E/(smax*F)
1.4 1.2 1 0.8 0.6 0.4 0.2 0
0.7
1.0
1.5
1.75
2.0 3.0 Drift [%]
4.0
5.0
6.0
Figure 4.17: Dissipated energy during seismic test on strengthened column[80] The cracking framework of the strengthened columns remains unchanged starting from a drift close to 1% because of the progressive grouping of the deformation in the interface area between HPFRC jacket and foundation with a manifestation of the partial pull-off of the jacket. The confinement effect carried out by the strengthening jacket prevents in any way the occurring of events of the concrete cover expulsion and the instabilization of the reinforcing bars, ensuring an increase of ductility in comparison to the similar unstrengthened specimens.
111
Index > 4 Applications > 4.3 Applying the strengthening technique It is useful to highlight how in cases of 3-sided jackets, the adhesion between the jacket and the traditional concrete remains good for both specimens: there is no recording of any detachment from the devices up to a drift of 1.25% and at the end of the test, for a drift of 6%, the values appear lower than 0.5 mm, essentially caused by the progress of the concrete cover ejection event on the no-jacket side. The results of experimental tests confirm the validity of the jacketing solution in the strengthening of existing reinforced concrete elements distinct of design only for vertical loads and marked by poor properties of materials, such as: low quality concrete and smooth surface reinforcing bars; and lacking constructive details, such as: stirrups with 90° lock closures and distant interaxes. This technique results, also valid for jacketing on three sides, suitable for the strengthening of external columns, for which the application of a full jacketing on the 4 sides can imply complex practicalities of execution connected to probable access difficulties near the façade of the building. The casing applied only on column-free side surfaces would allow a reduction in time and expense in terms of the cost of the operation, as well as making it much easier.
4.3.3.3
Strengthening of corroded columns
anode
cathode Solution level; 1m Saline solution E1
E2
E3
E4
Power supply
Figure 4.18: Scheme for accelerated corrosion process[83] Another reason for concern for reinforced concrete structures is the decrease in the useful life of elements in reinforced concrete, mainly because of the corrosion of the reinforcing bars. 112
Index > 4 Applications > 4.3 Applying the strengthening technique
The effects on structural behavior in elements attacked by corrosion of the reinforcement bars are multiple: The decrease of the resistant section of the bars, the reduction of the bearing load by the reinforcement bars, the decrease of the ductility of the structure, the creation of products of corrosion that create cracking of the concrete, are able to change in a substantial way the manner in which a structure collapses.[81] Lately some studies have been carried out on the validity of the solution of the HPFRC with regard to the increase of the bearing capacity of reinforced concrete columns with problems of corrosion of the reinforcement bars.[82][83] -40
Load [kN]
-60
120
F
Not corroded column Corroded column Jacketed column
-80
100
-100 80 -120 60
40 20
Drift [%]
0 -6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
-20 -40 -60
F
-80 -100 -120
Figure 4.19: Comparison of (column) horizontal load - displacement, drift diagram[84]
The results of tests on the jacketed specimen reinforce the validity of this strengthening solution: for both positive and negative stresses the maximum load results higher than that measured in the not [81]
Coppola Luigi. Concretum. Italian. McGraw-Hill, Mar. 2007. isbn: 978-88-386-6465-6. url: https :
//books.google.it/books?id=b2G4GAAACAAJ. [82] Serena Mostosi, Alberto Meda, Zila Rinaldi, and Paolo Riva. “Repair of RC columns with corroded reinforcement by means of high performance jacket”. In: Proceedings of the 4th International Workshop PROTECT2013 on Performance, Protection and Strengthening of Structures under extreme loading, August 26 - 27, 2013, Mysore, India. Mysore, India, Aug. 2013. [83] Alberto Meda, Serena Mostosi, Zila Rinaldi, and Paolo Riva. “Corroded RC columns repair and strengthening with high performance fiber reinforced concrete jacket”. In: Materials and Structures 49.5 (May 2015), pp. 1967–1978. issn: 1871-6873. doi: 10.1617/s11527-015-0627-1.
113
Index > 4 Applications > 4.3 Applying the strengthening technique corroded specimen. By examining the negative drift values, the direction in which the strengthened specimen presents a regular failing mode, the maximum load has an increase of 65% compared to that of the integral column and an increase of 118% compared to the column with corroded reinforcement bars. From the graphs it is noted how the behaviour of the strengthened specimen is typical of the sections characterized by a nucleus in traditional concrete and a high-performance FRC jacket. Once the maximum load has been reached the strength of the strengthened column is rapidly reduced considering that the tensile contribution of the HPFRC material begins to fail. This is because of the establishment of the macro-crack concentrated at the column-foundation interface. In subsequent cycles at peak load, for negative stresses, the resistance of the jacketed specimen is higher than the resistance of the whole specimen, thanks to the compression collaboration of the fibre-reinforced jacket. The specimen with HPFRC jacket does not exhibit symptoms of removal of the concrete cover or deformation due to instability of the bars for causes concerning the high confinement action imposed by the jacket. In Figure 4.19[84] is shown a comparison between the load curves - horizontal displacement for the three column specimens. In Figure 4.18[85] is shown a diagram for an accelerated process of corrosion. To conclude, the results of experimental tests prove the validity of the solution of jacketing with HPFRC also for the strengthening of columns with problems of corrosion of the longitudinal reinforcement bars, with the overall increase of the bearing capacity of the column with corroded bars with peak resistance higher than that of the not deteriorated specimen. Moreover, the use of the jacket is able to preserve the original column, increasing its durability, since the material of the jacket is a micro-concrete with indicator of infiltration of CO2 lower than that of a traditional concrete. 4.3.3.4
Applicability on columns
In situations of strengthening of columns with HPFRC material jacket, it is necessary to make the connection between column and foundation by means of a pocket of depth equal at least 5 cm in the foundation, and in any case sufficient to put in view the reinforcement bars of foundation. Inside the section of the column is inserted an electrowelded or harmonic steel net mesh of height [84]
Serena Mostosi, Alberto Meda, Zila Rinaldi, and Paolo Riva. “Riparazione di pilastri in CA con armature corrose
mediante incamiciature in calcestruzzo ad elevate prestazioni”. Italian. In: Atti del 27° Convegno Nazionale AICAP 2014: Strutture nel tessuto urbano. Progetto e realizzazione del nuovo e di interventi su esistente. 22-24 maggio 2014. AICAP. May 2014. [85] Alberto Meda, Serena Mostosi, Zila Rinaldi, and Paolo Riva. “Experimental evaluation of the corrosion influence on the cyclic behaviour of RC columns”. In: Engineering Structures 76 (Oct. 2014), pp. 112–123. issn: 0141-0296. doi: https://doi.org/10.1016/j.engstruct.2014.06.043.
114
Index > 4 Applications > 4.3 Applying the strengthening technique equal of about 20 cm. The effectiveness of the net has been investigated in recent studies.[86] If the positioning of a electrowelded net is not foreseen for the entire height of the column, it is suggested in any case to place a even a partial net near the concrete casting restart. The casting of the columns can be carried out in a single phase or alternatively in two phases:
• In case of a single phase, a formwork is put in place at full height and the casting of the high performance FRC material is done by pouring from a hole in the floor;
• In the second case, two phases, the formwork is positioned in the lower part and the cast is done from the bottom half of the jacket by pouring the material in the formwork. Then the upper half is again cast by a hole in the floor.
4.3.3.5
Design strength in compression-flexure
In the following paragraphs will be discussed the drawing of the M-N domain with rigorous method, simplified method - by points and the effect of the confinement.
4.3.3.5.1
M-N Domain: Rigorous method
The drawing of the bending moment-normal stress
interaction domain diagram for a section subject to compression-flexure, is performed using an iterative method that considers the solution of equations of equilibrium and congruence, estimating for each point the position of the neutral axis, the deformations and the stresses on the materials, the value of the axial action and the moment associated with it. At ULS, the failure of the column is determined step by step as the reaching of the ultimate tensile deformation of the FRC, to compression of the FRC again or of the traditional concrete.
Constitutive laws of the materials
It is advisable to adopt, for the schematization of the
constitutive laws, stress-block type bonds for the compression concrete and for the HPFRC and a elasto-plastic type bond for the steel. See Figure 4.20. [86]
Luca Cominoli, Alessandra Marini, and Alberto Meda. “Pareti di taglio rinforzate mediante incamiciatura con
calcestruzzi fibrorinforzati ad alte prestazioni”. Italian. In: Atti del 17° Congresso CTE Roma, 5-8 novembre 2008. CTE. 2008, pp. 531–538. isbn: 978-88-903647-3-0.
115
Index > 4 Applications > 4.3 Applying the strengthening technique nucleus concrete
h d3
εs2
AS3 S S fcd
σs1As1
x
AS2
b
S
fFcd,L
fcd
σs2As2
εs3 εFt,L εFt,I
Compressive design strength of traditional concrete
h-x
AS1
d2
Upper and lower FRC fFcd,S
αFcx
εFc,s εcc=εFc,L εs1
c
d1
αccx
S
Lateral FRC
σs3As3
fFtd,L
fFtd,I
fFcd,S Compressive design strength of the upper HPFRC
fFcd,L Compressive design strength of HPFRC on the sides
fFtd,I
Tensile design strength of the lower HPFRC
fFtd,L Tensile design strength of HPFRC on the sides
σsi
Stress on the bars
Figure 4.20: Strengthened section of column: stress and strain distribution at ULS[64]
M-N domain drawing Gradually increasing the position of the neutral axis, axial load and associated bending moment are estimated with Equation 4.19[64] and Equation 4.20[64] respectively: N = fcd · b · αcc · x + As1 · σs1 + As2 · σs2 + As3 · σs3 + + fF cd · [s · b + 2 · s · αF c · (x + s)] +
Equation 4.19[64]
− fFt d · [s · b + 2 · s · (h − x + s)] h αcc h − · x + As1 · σs1 − d1 + M = fcd · b · αcc · x · 2 2 2 h h h s + As2 · σs2 − d2 + As3 · σs3 − d3 + fF cd · s · b · + + 2 2 2 2 h αF c + 2 · fF cd · αF c · (x + s) · s · +s − · (x + s) + 2 2 x + s h s + fFt d · s · b · + + 2 · fFt d · s · (h − x + s) · 2 2 2
Equation 4.20[64]
The values of reinforcement section areas As,i are considered from time to time positive or negative depending on whether reinforcement is compressed or tensed respectively. Similarly, associated stresses are estimated on the basis of deformations, evaluated by congruence equations. 4.3.3.5.2
M-N Domain: Simplified method - Drawing by points
It is proposed a simplified
method that deals with the drawing of the M-N domain by estimating several notable points, 116
Index > 4 Applications > 4.3 Applying the strengthening technique evaluating axial action and resistant moment to the variation of the position of the neutral axis.[87]
Entirely tensed section
In the case of pure tension, i.e. fully tensed section (Figure 4.21),
the axial load can be estimated by the expression:
N = − (As1 + As2 + As3 ) · fyd − [2 · (h + 2s) · s + 2 · b · s] · fFt d
Equation 4.21[64]
The reinforcement bars are all yielded since for the HPFRC in tension deformation values are considered ≥ 1% and therefore much higher than the deformation at the elastic limit of any reinforcement bar steel. A single unique value is assumed for the tensile strength of the lateral, upper, and lower HPFRC, since it is the same material, so fFt d, L = fFt d,S = fFt d, I . Bars S
c
d1
AS1
εFt,s εFt,L εs1
FRC fFtd,S = fFtd,L
fydAs1
d2 h
d3
εs2
AS2 AS3
εs3 εFt,L εFt,I
S S
b
fydAs2
fydAs3
S
fFtd,I = fFtd,L
Figure 4.21: Stress and strain distribution on fully in tension column section[64]
Entirely compressed section If the section is subject to pure compression (Figure 4.22), the axial load can be estimated by the expression:
N = (As1 + As2 + As3 ) · fyd + b · h · fcd + [2 · (h + 2s) · s + 2 · b · s] · fF cd [87]
Equation 4.22[64]
Serena Mostosi, Consuelo Beschi, Alberto Meda, and Paolo Riva. “Experimental and analytical behaviour of
RC members strengthened by means of high performance jacket”. In: Proceedings of the 2014 2nd FRC International Workshop (1st ACI–fib Joint Workshop) Fibre Reinforced Concrete: from Design to Structural Applications, École Polytechnique de Montréal. July 24th-25th, 2014. July 2014. url: http://hdl.handle.net/10446/32361.
117
Index > 4 Applications > 4.3 Applying the strengthening technique Bars S
c
d1
AS1
d2
fydAs1
FRC fFcd,S = fFcd,L
fFtd,I = fFtd,L
fFcd,I = fFcd,L
fydAs2
d3
h
εFc,s εFc,L εs1
Nucleus concrete fcd
εs2
AS2 AS3
S S
b
fydAs3
εs3 εFc,L εFc,I S
Figure 4.22: Stress and strain distribution on fully in compression column section[64]
Compressed-bended section
For a section subjected simultaneously to axial action and
bending moment, the points of the interaction diagram are drawn by increasing the value of the neutral axis position and estimating the value of the bending moment and the axial load linked to each increase. The ultimate strength is determined step by step by identifying the failure mode, that is the tension crisis of the lower HPFRC or the compression crisis of the upper HPFRC. It is supposed as the last deformation in compression that of the FRC. Estimated for concrete with class higher than C50/60, it is in any case lower than that of the concrete of the nucleus, considered equal to 3.5‰. After estimating the actual stress on the reinforcement bars, the axial load and the relative bending moment are evaluated with the Equation 4.19[64] and the Equation 4.20[64] respectively. The values of the reinforcement bar section areas As,i , since the position of the neutral axis is known a priori, from time to time are considered positive or negative depending on whether the reinforcement bars are compressed or tensed respectively. Similarly, the relative stresses are estimated on the basis of deformations, so: • If the reinforcement bars are yielded, that is εs,i ≥ εsy =
fy d Es „
the term σs,i is replaced with
fyd ; • If the reinforcement bars are in the elastic field, that is εs,i ≤ εsy =
fy d Es ,
the term σs,i is
replaced by the expression εs,i · Es , with the deformations εs,i calculated by the congruence equations. 118
Index > 4 Applications > 4.3 Applying the strengthening technique 4.3.3.5.3
The effect of confinement
An effect not to be neglected of the jacket in HPFRC
material is the confinement that it practices on the concrete of the nucleus. The jacket develops a function similar to that of the stirrups causing a strong improvement of the performance of the initial concrete in terms of strength and in terms of ductility. Given the important increase in the ultimate deformation in compression of the confined concrete, it is usually noticed a strong increase of the ductility of the bended sections and above all of the compressed-bended ones. The presence of confinement has a much more remarkable effect as the more low-quality the traditional concrete is. The confinement of concrete causes a modification of the effective stress-strain relationship: higher strengths and higher critical deformations are obtained; It is used the relation σc − εc shown in Figure 4.23. A
σc
σ1 = fck,c
- unconfined fck,c
fck fcd,c A σ2
σ 3 ( = σ 2) εcu εc2,c
0
εcu2,c εc
Figure 4.23: Stress-strain relationship for confined concrete[28]
fck,c = fck fck,c = fck
σ2 · 1+5· fck
per σ2 ≤ 0.05 · fck
σ2 · 1.125 + 2.5 · fck
per σ2 > 0.05 · fck
2 f εc2,c = εc2 · cfck,kc εcu2,c = εcu2 · 0.2 · σ2 fc k where σ2 is the effective confinement tension at ULS.
Equation 4.23[28]
Equation 4.24[28]
Equation 4.25[28]
According to EN 1992-1-1 Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings, the confinement can be produced by properly closed stirrups that come to yield due to the transverse expansion of the compressed concrete. Effective confinement can be estimated by the following expression: 119
Index > 4 Applications > 4.3 Applying the strengthening technique
V ol stirrups fydw σ2 = 0.5 · α · ωwd = 0.5 · αn · αs · · fck V ol concr ete,con f ined fcd
Equation 4.26[28]
Assuming that the jacket in HPFRC performs a function similar to that of the stirrups, it is reasonable to estimate the increase of ductility and strength of the concrete of the nucleus by an adaptation of the Equation 4.23[28] , from which:
σ2 = 0.5 · α · ωwd fck
2 · b + h · s f Ft d = 0.5 · αn · αs · · b·h fcd
Equation 4.27[28]
where: b, h are the dimensions of the concrete nucleus, that is the section of the element to be strengthened; b, h the dimensions of the section near of the jacket axis, equal to the size of the nucleus plus the thickness s of the jacket; fFt d is the tensile design strength of the HPFRC; fcd is the compressive design strength of the concrete; αn is a coefficient that can be taken equal to 1, being the jacket similar to a continuous stirrup; αs is a coefficient that can be taken equal to 1, because the action of confinement continues along the step, unlike the action exerted by the stirrups, which are positioned discreetly, with a s step. In estimating the strength and deformation of confined concrete, it is considered fck equal to fc m FC ,
whereby the design strength of the confined concrete to be taken in the verifications fcd,c will
be equal to 0.85 ·
4.3.4
fc k, c γc .
Strengthening of nodes
The effects of earthquakes of the past have continually testified that the beam-column nodes constitute an area of enormous criticality in reinforced concrete frame constructions subjected to seismic actions. The way in which the nodal points behave, in fact, affects the behaviour of the total structural complex both regarding the strength and in terms of deformability. These are the mechanisms of failure that can happen: 120
Index > 4 Applications > 4.3 Applying the strengthening technique 1. Globally the presence of systems with strong beams-weak columns and locally the generation of fragile collapse mechanisms associated with poor protection of the nodal panel with fragile shear collapse. Both mechanisms to avoid; 2. The creation of plastic hinges in beams, typical event of complex beams/weak-column/strong with ductile collapse. Desirable mechanism; 3. The worsening by decrease in adherence bond between reinforcement bars and surrounding concrete material, conditioned by the type of reinforcement bars, ribbed or smooth bars, the length of anchorage and the existence of transverse reinforcement in the nodes, which could ensure a confinement action on the bars near the anchorages. This failure mechanism leads to an only apparent ductility of the structure, recognizable in another way as flexibility. As a result, the purpose of a strengthening operation on beam-column nodes is to change any fragile mechanisms, related to the shear failing of the nodal region, in mechanisms of ductile collapse, forcing the formation of plastic hinges at the extremities of the beams.
4.3.4.1
General concepts
The following paragraphs consider general aspects of corner and interior nodes.
4.3.4.1.1
Criticality of corner nodes The nodes exhibiting the most numerous criticalities
concerning seismic behaviour are external ones, particularly the corner nodes, primarily for the lack of confinement on one or two faces, for the unbalanced thrust of the collisions and because of a higher demand in terms of displacement related to overall torsional phenomena. Recently, some studies are focused on analyzing the behaviour of beam-column nodes built with typical construction details of the 60s-70s, especially the use of unindented reinforcement bars with unhooked terminal anchorages. It is highlighted the fragility of this type of nodes in the tests carried out on a reinforced concrete planar frame realized with typical details of the Italian construction practice of the years 60s-70s.[88] It is observed the generation of a shear failure mechanism different from the mechanism that is had in situations of rigid behaviours of [88]
G. M. Calvi, Guido Magenes, and Stefano Pampanin. “Studio sperimentale sulla risposta sismica di edifici a
telaio in cemento armato progettati per soli carichi da gravità”. Italian. In: Atti del X Congresso Nazionale ANIDIS: L’ingegneria Sismica in Italia, Potenza-Matera 9-13 settembre 2001. ANIDIS - Associazione Nazionale Italiana Di Ingegneria Sismica. Potenza-Matera: ANIDIS, Sept. 2001.
121
Index > 4 Applications > 4.3 Applying the strengthening technique the node, in which weak plan mechanisms are expected. This behaviour is proven by observations on the ways of collapsing of a large number of nodes in existing buildings hit by earthquakes in Italy. Numerous are the researches in literature that concern the examination of the seismic response of frames designed for the only vertical loads marked therefore by problems of structural deficiencies. Yet, although many researches analyze reinforcement ribbed bars anchored in the node[89][90][91][92][93] , only a limited part of them is focused on structural elements with smooth reinforcing bars and hook terminal anchorages, characteristic of the construction practices of the years ’60s-’70s.[94][95] The shear transfer mechanism in external beam-column nodes with smooth bars and without stirrups near the node itself, is based on the concepts of compressed strut, whose efficiency underlies in the strength of the concrete and in the anchorage solution chosen for longitudinal reinforcement bars. The strength of the node in cases of hook anchorages is driven by the removal of a concrete wedge caused by the thrust action imposed by the anchorages in compression and by the possible sliding of the reinforcement bars inside the nodal panel. It emerges therefore necessary even more than for the internal nodes, to take measures with strengthening solutions that allow to transfer the failure mechanisms outside the nodal panel so to [89]
Luis E. Aycardi, John B. Mander, and Andrei M. Reinhorn. “Seismic resistance of reinforced concrete frame
structures designed only for gravity loads: Experimental performance of subassemblages”. In: ACI Structural Journal 91 (5 Sept. 1994), pp. 552–563. doi: 10.14359/4170. [90] C. V. R. Murty, Durgesh C. Rai, K K. Bajpai, and Sudhir K. Jain. “Effectiveness of reinforcement details in exterior reinforced concrete beam-column joints for earthquake resistance”. In: ACI Structural Journal 100 (2 Mar. 2003), pp. 149–156. doi: 10.14359/12478. [91] Angelo Masi, Giuseppe Santarsiero, and Domenico Nigro. “Cyclic Tests on External RC Beam-Column Joints: Role of Seismic Design Level and Axial Load Value on the Ultimate Capacity”. In: Journal of Earthquake Engineering 17.1 (2013), pp. 110–136. doi: 10.1080/13632469.2012.707345. [92] Akanshu Sharma, Ramachandra Gudheti, K.K. Vaze, and Rolf Eligehausen. “Pushover experiment and analysis of a full scale non-seismically detailed RC structure”. In: Engineering Structures 46 (Jan. 2013), pp. 218–233. doi: 10.1016/j.engstruct.2012.08.006. [93] Saptarshi Sasmal, K. Ramanjaneyulu, Balthasar Novák, and N. Lakshmanan. “Analytical and experimental investigations on seismic performance of exterior beam–column subassemblages of existing RC-framed building”. In: Earthquake Engineering & Structural Dynamics 42.12 (Apr. 2013), pp. 1785–1805. doi: 10.1002/eqe.2298. [94] Stefano Pampanin, Guido Magenes, and Athol J. Carr. “Modelling of shear hinge mechanism in poorly detailed RC beam-column joints”. In: Proceedings of the fib symposium 2003: concrete structures in seismic regions, Athens, May 6-8, 2003. Ed. by Techniko Epimeleterio Hellados, Fédération internationale du béton, International Association for Bridge, and Structural Engineering. University of Canterbury. Athens, Greece: Technical Chamber of Greece, Jan. 2003. [95]
Franco Braga, Rosario Gigliotti, and Michelangelo Laterza. “R/C Existing Structures with Smooth Reinforcing
Bars: Experimental Behaviour of Beam-Column Joints Subject to Cyclic Lateral Loads”. In: The Open Construction and Building Technology Journal 3 (May 2009), pp. 52–67. doi: 10.2174/1874836800903010052.
122
Index > 4 Applications > 4.3 Applying the strengthening technique encourage a mechanism of ductile collapse.
4.3.4.1.2
Internal nodes
The use of high performance fibre-reinforced concrete jacketings is
efficient for the strengthening of internal beam-column nodes, where the strengthening of the nodal panel is carried out simultaneously with the intervention of strengthening of the column, making a single jacket, in order to eliminate a possible collapsing mechanism typical of strong beam-weak column.[96][97][98] Experimental cyclic test results show how using the high performance fibre-reinforced concrete jacketing technique, it is feasible to increase the strength of the beam-column nodes by achieving an adequate degree of ductility, especially appropriate in situations where an increase in the bearing capacity of the columns is also desired.
4.3.4.1.3
Corner nodes
The situation is more critical in cases of external nodes, particularly
of corner nodes. Cyclic tests on node specimens part of recent studies on the methods of various types of strengthening, demonstrate the great weakness of the reinforced concrete beam-column
[96]
Consuelo Beschi, Alberto Meda, and Paolo Riva. “Beam-Column Joint Retrofitting With High Performance Fiber
Reinforced Concrete Jacketing”. In: Proceedings of the 1° Workshop - Le nuove frontiere del calcestruzzo strutturale - The new boundaries of structural concrete. Università degli Studi di Salerno. April 22nd-23rd, 2010. Salerno, Italy: ACI Italy Chapter, Apr. 2010. isbn: 978-88-95028-55-2. [97] Consuelo Beschi, Alberto Meda, and Paolo Riva. “Beam-column joint retrofitting with high performance fiber reinforced concrete jacketing”. In: Proceedings of the 3rd International Conference Workshop PROTECT2011: Performance, Protection and Strengthening of Structures under Extreme Loading. Vol. 82. Applied Mechanics and Materials. 30 August - 1 September 2011. Trans Tech Publications, Sept. 2011, pp. 577–582. isbn: 9783037852170. doi: 10.4028/www.scientific.net/AMM.82.577. [98] Consuelo Beschi, Alberto Meda, and Paolo Riva. “Beam-Column Joint Retrofitting With High Performance Fiber Reinforced Concrete Jacketing”. Italian. In: Proceedings of ANIDIS 2011 - XIV Convegno Nazionale l’Ingegneria Sismica in Italia. 18-22 Settembre 2011. ANIDIS - Associazione Nazionale Italiana di Ingegneria Sismica. Politecnico di Bari, 2011. isbn: 978-88-7522-040-2.
123
Index > 4 Applications > 4.3 Applying the strengthening technique nodes made with the construction details of the years ’60s-’70s.[99][100][101][102][103][104][105] The specimens made according to the norms in force before the years ’70s, representative of the corner node of the first degree of a reinforced concrete structure, are distinguished by smooth reinforcement bars with hook terminal anchorages and lack of stirrups in the nodal panel. The strengthening technique involves the application of a high performance fibre-reinforced concrete jacket to specimens with identical geometrical properties and equivalent reinforcement details of the unstrengthened specimens. The tests consider the application of static loads in seismic combination, i.e. axial action on the column, bend moment and shear stress on the main beam, moment on the secondary beam, and then a history of horizontal cyclic displacements of rising amplitude in at the heading of the column till failure. In Figure 4.24 are shown comparisons between the results of experimental tests on unstrengthened and strengthened specimens. It is proved the high vulnerability of corner beam-column nodes built with emblematic construction details of the ’60s-’70s and the very important function of the phenomenon of sliding of the longitudinal reinforcement bars. The collapse of the unstrengthened [99]
Consuelo Beschi, Paolo Riva, and Alberto Meda. “Corner beam-column joints seismic retrofitting with high
performance fiber-reinforced concrete jacketing”. In: Proceedings of the 15th IAEE World conference on earthquake engineering. 15WCEE, 24-28 September 2012, paper N° 2128. IAEE (International Association for Earthquake Engineering). Lisbon, Portugal, Sept. 2012. [100] Chris G. Karayannis, Constantin E. Chalioris, and George M. Sirkelis. “Local Retrofit of Exterior RC BeamColumn Joints Using Thin RC Jackets—An Experimental Study”. In: Earthquake Engineering & Structural Dynamics 37 (Apr. 2008), pp. 727–746. doi: https://doi.org/10.1002/eqe.783. Consuelo Beschi, Paolo Riva, and Alberto Meda. “Corner beam-column joints retrofitting with HPFRC jacketing”.
[101]
In: Proceedings of the 3rd International Conference on Concrete Repair, Rehabilitation and Retrofitting, ICCRRR-3, 3-5 September 2012, Cape Town, South Africa. Ed. by Mark G. Alexander, Hans-Dieter Beushausen, Frank Dehn, and Pilate Moyo. Cape Town, South Africa: CRC Press - Taylor and Francis Group, Sept. 2012, pp. 437–438. isbn: 978-0-415-89952-9. Consuelo Beschi, Alberto Meda, and Paolo Riva. “Rinforzo di nodi trave-pilastro d’angolo con incamiciatura in
[102]
calcestruzzo fibro-rinforzato ad elevate prestazioni”. Italian. In: Atti del 19° Congresso CTE, Bologna, Italia, 8-10 novembre 2012. CTE. Nov. 2012. isbn: 978-88-903647-9-2. Consuelo Beschi, Paolo Riva, and Alberto Meda. “Rinforzo di Nodi Trave-Pilastro d’Angolo di Strutture a
[103]
Telaio in C.A. con Incamiciatura in HPFRC”. Italian. In: Atti del XV Convegno Nazionale ANIDIS: L’Ingegneria Sismica in Italia. ANIDIS - Associazione Nazionale Italiana di Ingegneria Sismica. Padova, Italia, Jan. 2013. isbn: 9788897385592. Consuelo Beschi, Paolo Riva, and Alberto Meda. “Studio sperimentale di tecniche per il rinforzo di nodi trave
[104]
pilastro d’angolo di strutture a telaio in ca”. Italian. In: Atti del 27° Convegno Nazionale AICAP 2014: Strutture nel tessuto urbano. Progetto e realizzazione del nuovo e di interventi su esistente. 22-24 maggio 2014. AICAP. May 2014. isbn: 978-8-88-859082-0. Consuelo Beschi, Paolo Riva, Giovanni Metelli, and Alberto Meda. “HPFRC Jacketing of Non Seismically
[105]
Detailed RC Corner Joints”. In: Journal Of Earthquake Engineering 19.1 (Jan. 2015), pp. 25–47. issn: 1363-2469. doi: 10.1080/13632469.2014.948646.
124
Index > 4 Applications > 4.3 Applying the strengthening technique specimens is the result of the collaboration between three modes of failure: beam side collapse with the introduction of a crack at the beam-node interface, collapse by shear of the node with diagonal cracks in the nodal panel and removal of the concrete cover in the lower part because of the thrust of the hooks of the extremities of reinforcement bars of the beams and last, the sliding of the reinforcing bars. The High Performance Fibre-Reinforced Concrete jacket of the structural elements allows to increase the strength of the node in comparison to the non strengthened solution of 40-45% for positive displacements and 30% for negative displacements. The residual strength after reaching the peak load is close to that of the unstrengthened specimen. Relative to the cracking framework, in the unstrengthened specimens are noted in the nodal panel diagonal crack openings greater than 3.5 mm, result of an extended deterioration of the node at the end of the test. Strengthened tests on the other hand, show to be valid in securing appropriate protection of the nodal panel with the appearance of a few capillary crack of a maximum opening of a few tenths of a millimetre and deterioration gradually concentrated in a single vertical crack at the beam-column interface. 60 50 40 30 20 10 0 -10 -20 -30 -40 -50 -60
0
30
60
90 120 150 180
0
1
2
3
Displacement [mm]
Horizontal load [kN]
Horizontal load [kN]
Displacement [mm] -210 -180 -150 -120 -90 -60 -30
-7
-6
-5
-4
-3
-2
-1
(a)
4
60 50 40 30 20 10 0 -10 -20 -30 -40 -50 -60
5 6 Drift [%]
-210 -180 -150 -120 -90 -60 -30
-7
-6
-5
-4
-3
-2
-1
0
30
60
90 120 150 180
0
1
2
3
(b)
4
5 6 Drift [%]
Figure 4.24: Results of cyclic tests for: (a) not strengthened nodes; (b) strengthened nodes[103] In the vicinity of the connection with the secondary beam, differently from unstrengthened specimens in which the removal of a large surface of concrete cover in the lower part of the node is evident, no deterioration is reported in each of the strengthened solutions. As a proof that the remaking of the node with HPFRC jacketing results performing in stopping the thrusts of the extremities of the hooked reinforcement bars of the beam. In conclusion, it can be said that elements constructed with smooth bars with hook anchors, without stirrups in the node and concrete of poor quality, require a strengthening operation concerning the horizontal loads, with the aim of moving the failure mechanism from a fragile shear 125
Index > 4 Applications > 4.3 Applying the strengthening technique collapse of the nodal panel to a more ductile one, with the introduction of a plastic hinge in the beeam. It is seen an optimisation of the seismic capabilities of specimens strengthened with highperformance FRC jackets, which do not show notable deterioration of the nodal panel. In addition, the pinching effect of hysteresis cycles is less evident. Finally it is considered interesting to pay attention to the behavior of the node proved roughly symmetrical in the two directions of load, with a clear advantage during seismic events. On the contrary, the tests show a limitation of the suggested technique, related to the premature removal of the jacket in HPFRC, which does not allow to fully take advantage of the potential of the strength increase provided by the jacket. To remedy this problem, it is recommended the use of connection components, such as plugs, between the old and new concrete. The use of connections can also be useful for the placement of a probable wire mesh. The insertion of a net around the node, which continues inside the beam, could also allow the limitation of the opening of the cracking between beam-node. 4.3.4.2
Applicability of the technique on nodes
Regarding the strengthening of beam-column nodes once the support has been prepared, perfect seal frameworks are placed at the bottom of the node. The casting by pouring is done of the column part under the node and beam part converging in it. The first casting’s frameworks are removed, the perfect seal frameworks are placed in the area above the node and the casting is done by pouring high performance fibre-reinforced concrete at the column’s part above the node. It is recommended the use of connecting pegs between the old and the new concrete in the vicinity of the node to prevent events of early removal of the jacket in HPFRC material from the traditional concrete. The use of connections may also be advantageous for the placement of a wire mesh if an additional increase in the shear strength of the beam was to be required. 4.3.4.3
Norms
In line with the Italian laws [54] , the resistance verification is carried out only for the not entirely confined nodes as described in paragraph § 7.4.4.3 of Decreto del Ministero delle infrastrutture 14 gennaio 2008 - Approvazione delle nuove norme tecniche per le costruzioni. According to this paragraph, a node is confined entirely confined if in all four vertical faces there is a beam. The confinement is considered realized when, on each face of the node, the section of the beam covers at least 3/4 the width of the column and, on both pairs of opposite faces of the node, the sections of the beams cover for at least 3/4 of the height (Figure 4.25(a) and (d)). 126
Index > 4 Applications > 4.3 Applying the strengthening technique
a) Interior
b) Exterior
d) Roof interior
c) Corner
e) Roof exterior
f) Roof corner
Figure 4.25: Typical beam-to-column connections[106] The internal and external nodes, called of façade or of corner, since they do not meet at least one of these conditions, belong to the category of the nodes not entirely confined for which it is necessary to verify both the diagonal tensile strength and the diagonal compressive strength Figure 4.25 (b,c,d,e).[106] 4.3.4.4
Strengthening of façade nodes
It is showed by simple methods the execution of a fairly precise evaluation of the strength of beam-column nodes strengthened with in FRC material jackets. The suggested expressions refer to experimental test results for internal beam-column nodes.[107][108] 4.3.4.4.1
Evaluation of the strength of unstrengthened façade nodes The controls to be
performed for the internal nodes not entirely confined are: Evaluation of the tensile strength s 2 2 p N N Vn − + ≤ k · fcd σnt = 2 · Ag Ag 2 · Ag
Equation 4.28[108]
where: Ag = column section; [106]
Joint ACI-ASCE Committee 352. ACI 352R-02: Recommendations for Design of Beam-Column Connections in
Monolithic Reinforced Concrete Structures. Ed. by John F. Bonacci and Sergio M. Alcocer. ACI and ASCE. ACI, June 2002. 37 pp. isbn: 9780870310874. Consuelo Beschi, Alberto Meda, and Paolo Riva. “Column and Joint Retrofitting with High Performance Fiber
[107]
Reinforced Concrete Jacketing”. In: Journal of Earthquake Engineering 15.7 (Sept. 2011), pp. 989–1014. doi: 10.1080/13632469.2011.552167. Consuelo Beschi, Alberto Meda, Paolo Riva, and Francesca Simonelli. “Rinforzo di nodi trave-pilastro con
[108]
incamiciatura in calcestruzzo fibro-rinforzato ad elevate prestazioni”. Italian. In: Atti del 26° Convegno Nazionale AICAP - Lo sviluppo delle opere in c.a. nel terzo millennio. 19 - 21 maggio 2001. AICAP, Jan. 2011, pp. 453–460.
127
Index > 4 Applications > 4.3 Applying the strengthening technique N = axial action in the upper column; fcd = compressive design strength of the concrete; k = considered coefficient equal to 0.3; Vn = total shear on the node, calculated as the difference between the pull force in the reinforcement bars of the beam amplified by an over-resistance factor γRd and the shear at the upper part of the node, that is: Vn = γRd · As,sup + As,in f · fyd − VSd
Equation 4.29[108]
where: γRd = over-resistance coefficient considered equal to 1.2; As,sup = area of the reinforcement bars at the upper part of the node; As,in f = area of the reinforcement bars at the lower part of the node; fyd = yielding design tension of the reinforcement bars; VSd = shear stress at the upper part of the node. Evaluation of the compressive strength s 2 N Vn N + + ≤ 0.5 · fcd σnc = 2 · Ag 2 · Ag Ag
Equation 4.30[108]
Generally this verification is almost always fulfilled. The strengthening of the node by jacketing in HPFRC material, strongly increases the resistance thanks to the contribution of the FRC in tension. 4.3.4.4.2
Evaluation of the strength of strengthened façade nodes The jacketing of the
node in HPFRC material, transmits to it a certain degree of confinement. The verification on the strengthened node can be considered as a completely confined node verification in which in evaluated an average weighed tensile strength on the concrete of the unstrengthened column and on the FRC of the strengthening jacket. For the strengthened node, the Equation 4.28[108] becomes: s √ 2 2 k · fcd · Ag + fFt d · Ag0 N N V n ≤ − + σnt = 2 · AT AT AT 2 · AT where: k = 0.3; 128
Equation 4.31[108]
Index > 4 Applications > 4.3 Applying the strengthening technique fFt d = tensile design strength of the HPFRC material, given by the characteristic tensile strength fFtk divided by the coefficient in tension γF ; AT = Ag + Ag0 with Ag = area of the section of the unstrengthened column; Ag0 = area of the jacket in HPFRC material applied to the column (Figure 4.26 (a) ). bc,s Ag
s
A'g
s
C1 s
bc,s
VC
M1
z1
hb
bb
hp,s
Hp,s
T1
C2 z2
M2 VC
Hc
T2
s
Bc,s
Lbn
bc,i
Lb (a)
Lbn Lb
(b)
Figure 4.26: (a) Strengthened column section; (b) Forces to calculate strength of the node[117] The shear action in the node is estimated using the principles of Hierarchy of Resistances: Vn =
M1 M2 + − VC z1 z2
Equation 4.32[108]
where: M1 and M2 are the resistant moments of the beams, Figure 4.26 (b) ; z1 is equal to 0.9 · db for the original section and 0.9 · hb for the strengthened section, with hb = height of the beam section and db = useful height; z2 is equal to 0.9 · db in both cases. The shear action on the column is defined by the expression: VC = (M1 + M2 ) ·
1 Lb · Lbn HC
where: Lb = beam length; Lbn = net beam length; HC = column height. 129
Equation 4.33[108]
Index > 4 Applications > 4.3 Applying the strengthening technique 4.3.4.5
Strengthening of corner nodes
This paragraph provides guidance regarding the verification of corner nodes before and after strengthening.
4.3.4.5.1
Preamble The considerations on the strength of strengthened nodes with jackets in
HPFRC material are valid in the absence of events of detachment of the jacket. These formulas can be used to design the strengthening provided that clips or metal connectors are adopted for the connection between the concrete of the HPFRC jacket and the substrate, so as to fully utilize the benefits associated with the increase of strength conferred by the jacket.
4.3.4.5.2
Criticality of corner nodes for calculations The behavior of nodes under cyclic
actions affects the response of the entire structural system. The farer the design criteria are to what is stated in the recent seismic standards the more problematic the elements will be. See Figure 4.27. The strength of nodes designed according to Italian building practices of the years ’60s-’70s is influenced by various phenomena contributing to the failure mechanism. For example: expulsion of concrete due to the thrusts of the anchorages of the reinforcement, sliding of the reinforcement bars, shear crisis of the nodal panel. It is difficult to calculate the contribution of each mechanism. Displacement at the top
Frame Shear hinges Plastic hinges
Figure 4.27: Global collapsing mechanism for a frame structure in reinforced concrete[117] 130
Index > 4 Applications > 4.3 Applying the strengthening technique It is proposed now an analytical model that takes into account the phenomena indicated. 4.3.4.5.3
Evaluation of the strength of unstrengthened corner nodes Two simplified evalu-
ation methods are considered.[109] In the first method, called the PSLM - Principal Stress Limitation Model, the strength of the node is governed by the maximum main tensile stress reached in the nodal panel. The second method, called MSSTM - Modified Softened Strut-and-Tie Model is a re-elaboration of the strut-and-tie model suggested for confined nodes.[110] PSLM - Principal Stress Limitation Model
Many authors recommend to estimate the shear
strength of a node by following the limitation of the maximum value of the main tensile stress achieved in the nodal panel. This suggestion, when are considered nodes without confining reinforcement, is correct. The primary stresses in the node are estimated through the relationships of the continuum mechanics. The main tensile stress pt corresponding to the first cracking of the node during the first loading cycle is estimated by the following expression: pt = k 1 ·
p
fc0
Equation 4.34[109]
where: fc0 is the cylindrical compressive strength of the concrete; k 1 is an assumed coefficient between 0.2 and 0.5 depending on the details of the reinforcement in the node, considering: • Type of bar, smooth or ribbed; • Type of anchorage, with hook, at 90°, with internal or external folding; • Presence or not of stirrups in the node. For corner nodes with smooth bars, hook anchorages and lack of stirrups in the node, the proposed value of k 1 is equal to 0.2. [109]
Giovanni Metelli, Francesco Messali, Consuelo Beschi, and Paolo Riva. “A model for beam-column corner joints
of existing RC frame subjected to cyclic loading”. In: Engineering Structures 89 (2015), pp. 79–92. issn: 0141-0296. doi: https://doi.org/10.1016/j.engstruct.2015.01.038. Shyh-Jiann Hwang and Hung-Jen Lee. “Analytical model for predicting shear strengths of exterior reinforced
[110]
concrete beam-column joints for seismic resistance”. In: 96 (5 Sept. 1999), pp. 846–857. doi: 10.14359/739.
131
Index > 4 Applications > 4.3 Applying the strengthening technique The maximum resistant shear stress of the nodal panel, considered uniform, is determined with the following expression:
s ν jh = k 1 ·
p
fc0
1+
·
fa p k 1 · fc0
Equation 4.35[109]
where: fa is the average compression stress acting on the column section. The strength of the nodal panel is evaluated with this formula:
Vjh = ν jh · b j · h j
Equation 4.36[109]
where: b j is the effective width of the node; h j is the distance between the outermost dispositions of the column reinforcement.
MSSTM - Modified Softened Strut and Tie Model
The model proposed in[111][112] is an
adaptation of the Softened Strut-and-Tie Model. It considers the overlap of three strut-and-tie mechanisms forming inside the nodal panel and provide for the presence of compressed diagonals of non-cracked concrete and ties consisting of stirrups and longitudinal reinforcement bars of the column (Figure 4.28). In order to evaluate the ultimate shear strength of the node, an iterative procedure is carried out in which the equilibrium, congruence and the constitutive bonding equations of the materials must be satisfied at each step (Figure 4.29). [111]
Paolo Riva, Giovanni Metelli, Consuelo Beschi, and Francesco Messalli. “Modellazione di nodi trave-pilastro
esterni di telai in cemento armato soggetti ad azioni cicliche”. Italian. In: Atti del XIV Convegno Nazionale ANIDIS: L’Ingegneria Sismica in Italia. 18-22/09/2011. Bari, Italia. ANIDIS - Associazione Nazionale Italiana di Ingegneria Sismica. Bari, Italia, Sept. 2011. isbn: 978-88-7522-040-2. Paolo Riva, Consuelo Beschi, Giovanni Metelli, and Francesco Messali. “A model for beam-column corner joints
[112]
of existing RC frame under cyclic loading”. In: Proceedings of the 4th International Symposium Bond in concrete 2012: General aspects of bond. 17-20 June 2012. Brescia, Italia. Ed. by John W. Cairns, Giovanni Metelli G., and Giovanni A. Plizzari. Vol. 1. 17-20/06/2012. Heriot-Watt University. Brescia, Italia: Publisher Creations, June 2012, pp. 225–232. isbn: 978-88-907078-1-0.
132
Index > 4 Applications > 4.3 Applying the strengthening technique
Strut
Tie
Figure 4.28: Strut-and-tie SSTM model[111]
The ultimate strength of the node is reached when the calculated stress is equal to the maximum value that the cracked concrete can withstand in compression:
σd = σd,lim = ζ · fc0
Equation 4.37[109]
1
Equation 4.38[109]
ζ=
0.8 +
0.34·εr 0.002
≤1
where: σd is the average main stress in the d direction of the diagonal strut; ζ is the softening coefficient; fc0 is the cylindrical compressive strength; εd and εr are the average main deformations in the directions d and r (perpendicular to d). 133
Index > 4 Applications > 4.3 Applying the strengthening technique
Astr, f'c, ε0, θ, ΔD
Di = Di-1 + ΔD D Astr
σd,max =
σd,max f'c
ζ1 =
εd = ζ ε 0 NO
εr = - εdcot2θ ζ2 =
5.8 f'c
1
≤
1 + 400 εr
0.9 1 + 400 εr
ζ1 ≈ ζ2 YES Vjh = Di cosθ
Figure 4.29: Flowchart for iterative calculation of the shear strength of a node[111] In relation to the type of nodes considered, the strut starts to form outside the nodal region. The inclination of the strut is supposed to be equal to:
hp θ j = arctan bp
Equation 4.39[109]
with h p = hb +
hc −c 4
Equation 4.40[109]
b p = hc −
ac −c 2
Equation 4.41[109]
N · hc ac = 0.25 + 0.85 · Ag · fc0
Equation 4.42[109]
where: hb is the height of the beam; hc is the width of the column; 134
Index > 4 Applications > 4.3 Applying the strengthening technique c is the concrete cover; ac is the height of the compressed portion of the column section; N is the axial action in the column; Ag is the area of the column. The width of the concrete strut in the node is evaluated with this formula: ac0 = ac · sinθ Validation of the proposed methods
Equation 4.43[109]
To check the validity of the indicated expressions for
the evaluation of the strength of corner nodes, comparisons with experimental data available in the literature have been performed.[113][114][115][116] It appears that the PSLM method, whose coefficient is calibrated on the basis of the experimental results for this type of nodes, provides a reliable estimation of the experimental results. The other way around, the SSTM method overestimates the experimental results and thus results inadequate for the study of this type of nodes. The changes made, MSSTM, reduce the average strength evaluation of 40% in average, allowing to obtain a better correspondence with the experimental data. 4.3.4.5.4
Evaluation of the strength of strengthened corner nodes
This paragraph provides
indications for the evaluation of the strength of corner nodes and converging elements in it before and after strengthening with HPFRC material jacket.
[113]
It is considered a node with the same geometrical and reinforcement characteristics of the unstrengthened node specimens as shown in Figure 4.30.[117] [113]
Franco Braga, G. De Carlo, G. F. Corrado, Rosario Gigliotti, Michelangelo Laterza, and Domenico Nigro.
“Meccanismi di risposta di nodi trave-pilastro in c.a. di strutture non antisismiche”. Italian. In: Atti del X Congresso Nazionale ANIDIS: L’ingegneria Sismica in Italia, Potenza-Matera 9-13 settembre 2001. ANIDIS - Associazione Nazionale Italiana Di Ingegneria Sismica. Potenza-Matera: ANIDIS, Sept. 2001. Umut Akgüzel and Stefano Pampanin. “Effects of variation of axial load and bi-directional loading on the FRP
[114]
Retrofit of existing BC joints”. In: Proceedings of the 14th World Conference on Earthquake Engineering. Beijing, China. Beijing, China, Nov. 2008. Weng Yuen Kam, Patricio Quintana Gallo, Umut Akguzel, and Stefano Pampanin. “Influence of slab on the
[115]
seismic response of sub-standard detailed exterior reinforced concrete beam column joints”. In: (Jan. 2010). Retrofit solutions for New Zealand. Shigeru Hakuto, Robert Park, and Hitoshi Tanaka. “Seismic Load Tests on Interior and Exterior Beam-Column
[116]
Joints with Substandard Reinforcing Details”. In: ACI Structural Journal 97.1 (2000). doi: 10.14359/829. Consuelo Beschi, Giovanni Metelli, and Paolo Riva. “Retrofitting of beam-column exterior joint with HPFRC
[117]
jacketing”. In: Proceedings of the 2° edition of ACI Italy Chapter Workshop: The new boundaries of structural concrete. Ancona, 15-16 settembre 2011. ACI Italy Chapter, Jan. 2011.
135
Index > 4 Applications > 4.3 Applying the strengthening technique
N 4 H
1380
2
Φ16 L = 2540 mm
3
Φ12 L = 2510 mm
80
240 St. #8@200
5 300 3
4
5
6
6
Section B-B
500
B 3000
80
3
460
Φ16 L = 1620 mm 500
2
1
F B
1 1
4
Φ16 L = 2560 mm
5
Φ12 L = 2510 mm
6
Φ16 L = 2560 mm
60
60 260
300
260
A
300
1120
A
St. #6@150
Section A-A 300
1960 2260
Figure 4.30: Geometry of a beam-column specimen[117]
It is considered to strengthen the structural elements with a jacket of thickness equal to 30 mm. For the column it is supposed an intervention with thickness 40 mm. As shown in Figure 4.31, for the beam are assumed two ways of strengthening with U-jacket and two other ways of strengthening only on the sides. In the U-jacket solution it is supposed to use a 30 mm layer of self-compacting HPFRC material for the whole jacket, or alternatively to strengthen using a layer of 30 mm thickness of self-compacting HPFRC material at the intrados surface of the beam and two layers of 30 mm of thixotropic HPFRC material on the sides.
Suggested with the aim of preventing a strong beam-weak column mechanism, a second type of strengthening involves the application of two layers of 30 mm self-compacting or thixotropic HPFRC material only on the sides of the same beam. 136
Index > 4 Applications > 4.3 Applying the strengthening technique The benefit of the use of thixotropic HPFRC, lies in the fact that the strengthening operation is simple and rapid. The use of connectors is highly recommended to guarantee the adherence between the new and old concrete. Solution 3
500
500
Solution 4
HPFRC Thixotropic HPFRC
30
30
500
Solution 2
500
Solution 1
30 300 30
30 300 30
30 300 30
30 300 30
360
360
360
360
(a)
(b)
(c)
(d)
Figure 4.31: Beam strengthening solutions: (a) Self-compacting HPFRC; (b) Self-compacting HPFRC at the bottom and thixotropic on the sides; (c) Self-compacting HPFRC on the sides; (d) Thixotropic HPFRC on the sides only[117]
Strengthening of the column In Figure 4.32 the M-N diagrams are shown for the unstrengthened section of the column and for the strengthened one with a jacket made with self-compacting HPFRC material, using two different thicknesses, of 30 and 40 mm. 700
M [kNm]
4Φ16 300
600
Base column
300
500 400
30 300 Retrofitted column 30 30 mm jacket
300 200
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
-1000
100
40 300 N [kN] Retrofitted column 40 40 mm jacket
Figure 4.32: M-N interaction diagram for a column[117] 137
4Φ16
360 4Φ16
380
Index > 4 Applications > 4.3 Applying the strengthening technique Strengthening of the beam For the evaluation of the increase in the flexural capacity of the beam with the different strengthening techniques considered, simplified analytical formulations based on the diagrams in Figure 4.33 are used for positive and negative moments. Concrete nucleus fcd
εsc
Ascσsc
fFcd,L
0.8x
εcc
HPFRC
h
fFtd,L
εst εFt,L b
Astσst
εFt,I = 1%
fFtd,I Concrete nucleus
εFt,L = 1% εsc
HPFRC fFtd,L
h
Astσst
εsc εcc εFc,I
b
0.8x
fFcd,L
Ascσsc
fFcd,I
Figure 4.33: Positive and negative stresses calculation diagram[117]
Strengthening of the unreinforced beam-column node The verification the unstrengthened node is performed with Equation 4.28[108] in relation to the scheme in Figure 4.34 (a). The shear action in the node is equal to: Vn =
Mb,y − Vc zb
where: Mby is the maximum resistant moment in the beam; z b is the arm internal couple. The shear action on the column Vc is determined with the expression:: 138
Equation 4.44[117]
Index > 4 Applications > 4.3 Applying the strengthening technique
Vc = Mb,y ·
1 L · Lbn H
Equation 4.45[117]
where: L is the length of the beam; Lbn is the net length of the beam; H is the height of the plane.
VC
VC
T
T Vn
Vn Mb,y
Vn
zb
H
C
VC
Mb,y
Vn
zb
H
C
VC VC
VC bc
bc
Lbn
Lbn Lb
Lb (a)
(b)
Figure 4.34: F orces acting on a (a) unstrengthened node and (b) strengthened node[117] Strengthening of the reinforced beam-column node For the verification the strengthened node wit is used Equation 4.31[108] , assuming both a factor k equal to 0.3, as expected by the current norms, also a factor of 0.2 in accordance with the PSLM method. 4.3.4.5.5
Remarks
Taking into consideration the case in which the strengthened section is
capable of developing the entire bearing capacity, the numerical curve provides higher resistance values than those reached by the test specimen for both positive and negative stresses. At a drift equal to -0.25% a crack appears in the nodal panel at the beam-node interface at the lower part of the beam and at a drift equal to +0.25% a similar crack is formed at the upper part of the beam at the beam-node interface. 139
Index > 4 Applications > 4.3 Applying the strengthening technique For higher drift values, when the contribution in tension of the jacket is no longer there, the residual resistance tends to that of the unstrengthened section, evaluated by the PSLM and MSSTM method. For negative stresses, the residual resistance tends to that of the unstrengthened specimen in the case of shear failure of the nodal panel. To estimate the peak load, taking these two aspects into consideration:
• The cracked section is considered neglecting the section part above the formed crack at the beam-node interface, which does not give any contribution to traction. • The tensile stress in the upper bars is assumed equal to that of the bars of the unstrengthened section marked by shear crisis of the node - this is because the reinforcement bars at the peak are not yielded.
- the numerical analysis does a good approximation of the negative peak load if the PSLM method is adopted, while does underestimate the load by 10% when considering the MSSTM method. It is stressed the need to implement connection elements between the substrate and the concrete of the jacket in order to avoid the detachment of the jacket itself so as to be able to exploit all the resistant capacity of the node and use the formulas indicated for design and verification of the strengthening operation.
4.3.5
Strengthening of masonry
The low tensile strength of the masonry makes buildings built with such material particularly vulnerable to seismic actions. This vulnerability is aggravated by the failure to adopt appropriate constructive details or even by improper structural organisation. With the exception of the worship structures or more generally the buildings subordinated by architectural constraint, the structures in masonry often are found in the field of the residential building. Several studies have shown that, after the 40 years of life, a construction normally requires several renovating operations, for example structural, energetic, etc., to continue to have updated quality standards. The structures built in the years ’60s and in the ’70s need today renovating interventions. Among the various interventions, it is also necessary to carry out seismic improvement operations of the buildings. 140
Index > 4 Applications > 4.3 Applying the strengthening technique The optimisation of seismic behaviour in the construction plane could be achieved by implementing structural interventions to encourage a box behaviour of the building[118][119] , in order to properly benefit from the resistance in the plane of the walls that make up the building. To be able to take advantage of this global mechanism it is appropriate that the walls, used to serve as bracing for the structure, should efficiently be connected to each other through a sufficiently rigid plane diaphragm. In addition to the presence of a performing bond between the vertical members of the building, it is in any way appropriate that the resistance in the floor of the bearing walls be sufficient when compared to the demand for resistance resulting from the seismic action. The optimisation of the resistance of the walls can be achieved through the adoption of different techniques that, in recent years, have been the basis of several studies. These are the technical solutions traditionally adopted for strengthening:
1. Strengthening with coatings reinforced with metallic meshes, with polymeric fibres or with glass fibres;[120][121][122][123] 2. Usage of shotcrete concrete, strengthened with metallic meshes;[124][125][126] [118]
Ezio Giuriani and Alessandra Marini. “Coperture scatolari antisismiche”. Italian. In: 169 (2011). Ed. by De
Lettera Editore, pp. 26–45. issn: 1593-3970. Paulo B. Lourenço, Nuno Mendes, Luís F. Ramos, and Daniel V. Oliveira. “Analysis of Masonry Structures
[119]
Without Box Behavior”. In: International Journal of Architectural Heritage 5.4-5 (July 2011), pp. 369–382. doi: 10.1080/15583058.2010.528824. Natalino Gattesco and Ingrid Boem. “Experimental and analytical study to evaluate the effectiveness of an
[120]
in-plane reinforcement for masonry walls using GFRP meshes”. In: Construction and Building Materials 88 (July 2015), pp. 94–104. issn: 0950-0618. doi: 10.1016/j.conbuildmat.2015.04.014. [121] C.-M Aldea, Barzin Mobasher, and N. Jain. “Cement-Based Matrix-Grid System for Masonry Rehabilitation”. In: ACI Spring Convention 244 (Jan. 2007). Special Publication, pp. 141–156. doi: 10.14359/18757. Mohamed A. ElGawady, Pierino Lestuzzi, and M. Badoux. “A review of conventional seismic retrofitting
[122]
techniques for URM”. in: Proceedings of the 13th International Brick and Block Masonry conference. Amsterdam, July 4-7, 2004. Amsterdam, Netherland, 2004, pp. 1–10. Gian Michele Calvi and Davide Bolognini. “Seismic response of reinforced concrete frames infilled with
[123]
weakly reinforced masonry panels”. In: Journal of Earthquake Engineering 5.2 (Apr. 2001), pp. 153–185. doi: 10.1080/13632460109350390. D. W. Robinson and Lawrence F. Kahn. Interface bonding of shotcrete reinforced brick masonry assemblages:
[124]
Volume 1. Tech. rep. Technical Report, 1981-1982. Atlanta: Georgia Institute of Technology, Sept. 1982. 146 pp. D. W. Robinson and Lawrence F. Kahn. Interface bonding of shotcrete reinforced brick masonry assemblages:
[125]
Volume 2. Tech. rep. Technical Report, 1981-1982. Atlanta: Georgia Institute of Technology, Sept. 1982. 188 pp. L Kahn. “Shotcrete retrofit for unreinforced brick masonry”. In: Proceedings of the 8th WCEE World Conference
[126]
on Earthquake Engineering. San Francisco, California, 1984. Vol. 1. San Francisco, California, USA, 1984, pp. 583– 590.
141
Index > 4 Applications > 4.3 Applying the strengthening technique 3. Insertion of mortar paste or resins;[127] 4. Strengthening with the application of FRP stripes/layers;[128][129][130] 5. Insertion of steel or concrete bracings, connected to the pre-existing walls.
The use of reinforced coatings shows various advantages such as the low cost, the limited degree of preparation necessary for the making and, when the coating has small thicknesses, the limited increase of the overall mass of the structure. Among the handicaps of this solution is the loss of time due to the placement and fixing of the reinforcement to the wall to be strengthened. Another drawback is if the coating is reinforced with metallic reinforcements, the need to assure a thickness of the cover to guarantee the degree of durability desired by the current norms:
• Decreto del Ministero delle infrastrutture 14 gennaio 2008 - Approvazione delle nuove norme tecniche per le costruzioni (2008)
• EN 1992-1-1 Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings (2005)
[127]
Luigia Binda, C. Modena, G. Baronio, and A. Gelmi. “Experimental qualification of injection admixtures used for
repair and strengthening of stone masonry walls”. In: Proceedings of the 10th International Brick and Block Masonry Conference. Ed. by A. Huizer, N.G. Shrive, International Brick and Block Masonry Conference, and Masonry Council of Canada. Vol. 2. 5-7 July, 1994. Calgary, Alberta, Canada, July 1994, pp. 539–548. Thanasis C. Triantafillou. “Strengthening of masonry structures using epoxy-bonded FRP laminates”. In: Journal
[128]
of composites for construction 2.2 (1998), pp. 96–104. issn: 1090-0268. doi: 10.1061/(ASCE)1090-0268(1998)2: 2(96). Maria Rosa Valluzzi, D. Tinazzi, and Claudio Modena. “Shear behavior of masonry panels strengthened by
[129]
FRP laminates”. In: Construction and Building materials 16.7 (Oct. 2002), pp. 409–416. issn: 0950-0618. doi: https://doi.org/10.1016/S0950-0618(02)00043-0. Miha Tomaževič, Iztok Klemenc, and Polona Weiss. “Seismic upgrading of old masonry buildings by seismic
[130]
isolation and CFRP laminates: A shaking-table study of reduced scale models”. In: Bulletin of Earthquake Engineering 7.1 (Feb. 2009), pp. 293–321. issn: 1573-1456. doi: 10.1007/s10518-008-9086-1.
142
Index > 4 Applications > 4.3 Applying the strengthening technique The results shown below show a summary of experimental researches[131][132][133][134] elaborated to analyze the feasibility of the use of coatings reinforced with steel fibres for strengthening of elements in masonry. Differently from the basic coatings the solution presented announces the use of steel fibres of moderate length, l f = 35 mm, as optional reinforcement to the normally used nets. The coating is composed of a high performance mortar which, besides having transpirant and waterproofing characteristics, exhibits high mechanical performance both in compression and tension. The use of steel fibres as an exclusive reinforcement component makes it possible to produce coatings with very small thicknesses, e.g. 20-30 mm. An additional benefit comes from the high tensile strength of the mortar. Actually the fibrous reinforcement allows to have a performance control of the cracking in normal service situations.
The study is concentrated on the deep understanding of an adequate solution to the application of coating reinforced with fibres on masonry walls built with full or with perforated bricks. The elaborated solution is carried out on walls realized in real scale of dimensions 3x2 m, which are subjected to cyclic loading tests able to resemble the conditions to which are subjected the walls of the constructions. Through experimental tests it is demonstrated how the use of the solution presented allows to optimise the behaviour of the walls in masonry both relative to the resistance and with regard to the initial stiffness. The solution presented emerges also valid for walls in masonry healed after a strong deterioration.
The specimens are tested by submitting them to a cyclically variable horizontal load and to a constant vertical load. The purpose of the tests is to simulate the typical behaviour of a backbone bearing wall, located inside a masonry construction formed by two storeys above ground. [131]
Luca Facconi, Antonio Conforti, Fausto Minelli, and Giovanni A. Plizzari. “Improving shear strength of
unreinforced masonry walls by nano-reinforced fibrous mortar coating”. In: 48.8 (June 2014), pp. 2557–2574. issn: 1871-6873. doi: 10.1617/s11527-014-0337-0. Luca Facconi. “Fiber reinforced concrete and mortar for enhanced structural elements and repair of masonry
[132]
walls”. PhD thesis. Brescia, Italy: Università degli Studi di Brescia, May 2014. 285 pp. isbn: 978-88-548-7010-9. url: http://www.aracneeditrice.it/aracneweb/index.php/pubblicazione.html?item=9788854870109. Luca Facconi, Antonio Conforti, Fausto Minelli, and Giovanni Plizzari. “Strengthening and Repairing Unreinforced
[133]
Masonry Walls by Nano-Composite Steel Fiber Reinforced Mortar Overlays”. In: Proceedings of the 4th International Workshop PROTECT2013 on Performance, Protection and Strengthening of Structures under extreme loading, August 26 - 27, 2013, Mysore, India. Mysore, India, Aug. 2013. Luca Facconi, Antonio Conforti, Fausto Minelli, and Giovanni Plizzari. “Shear strength improvement of unrein-
[134]
forced masonry walls by means of High Performance steel fibre reinforced mortar”. In: Proceedings of the 8th RILEM International Symposium on Fiber Reinforced Concrete: challenges and opportunities (BEFIB 2012). Ed. by Joaquim A.O. Barros. RILEM. Guimarães, Portugal: RILEM Publications SARL, Jan. 2012. isbn: 9782351581322.
143
Index > 4 Applications > 4.3 Applying the strengthening technique In addition two walls in perforated masonry bricks are tested; Test on wall initially unstrengthened tested until failure, after which, the wall is strengthened with two layers of coating and then is proceeded to the execution of the second test. The results of the tests are deduced from the development of the cycles executed in the direction of load taken conventionally as positive. The use of the strengthening solution presented allows to increase the maximum capacity (V+peak ) of the walls in full brick masonry of a quantity (∆V+peak ) that varies within the range 23-49%. After the application of the coating, the collapse of the specimen passes through a flexure-shear mechanism, seen in the unstrengthened specimen, to one by flexure with rocking. The use of a SFRM coating makes it possible to strongly increase the initial stiffness when compared to the unstrengthened wall. The results demonstrate how the use of only one layer is enough to achieve results comparable to those seen for walls strengthened with two layers of coating.
Finally, it results that the increase of stiffness in the phase of elastic behaviour of the walls can allow the optimization of the structure’s behaviour to the serviceability limit state. In fact, a higher initial stiffness of the structure involves less deformations and, consequently, fewer damages in case of a seismic phenomenon of reduced intensity. Seismic design acceleration of the structure is positioned in the proximity of the horizontal plateau of the elastic response spectrum. The reinforcement technique presented leads to the optimisation of the capacity and to the total restoration of the initial stiffness even in the cases in which the coating is used to restore pre-damaged walls.
4.3.5.1
Applicability of the strengthening on masonry
The use of the suggested consolidation solution for masonry requires the implementation of the following applicative procedure: 1. Initially, if the masonry is made of full bricks, it is advisable to increase the roughness of the surface so to increase the adherence between the coating and the masonry. The operation can be performed using chisel and hammer or through an automatic grinder. In the case of masonry with perforated blocks, the increase in roughness is not generally necessary. 2. Then the masonry is wetted with water until it is completely saturated. 3. After that, a first layer of mortar without steel fibres of about 5-6 mm thickness is applied to the wall. 144
Index > 4 Applications > 4.3 Applying the strengthening technique 4. Coating-masonry connections are fixed to the masonry surface without holes of the bricks. In cases of full bricks masonry, the connections are composed of a self-tapping screws with anchorage plate. In cases of perforated bricks, the anchorage requires the insertion of an appropriate plastic rawlplug to lock the screw in the chambers of the brick. 5. Finally the subsequent layers of high performance fibre-reinforced mortar are applied. 6. After the application of the coating, the masonry surface is kept wet for at least 5-7 days by water nebulisation.
4.3.5.2
Strengthening of walls with fibre-reinforced coatings
In this paragraph will be shown an analytical approach for the evaluation of the shear strength in the plane of masonry panels strengthened through coatings consisting of fibre-reinforced mortars (FRM). The coating can be applied on either sides of the wall. The high residual tensile strength transmitted from the fibres to the mortar allows to use very limited thicknesses of the coating layers. For the technique to be valid, the coating layers should be anchored to the masonry through metal connectors introduced in the depth of the coating layer (Figure 4.35).
Coating
RC cap beam (b) SFRM coating
Steel dowel with plate
All-thread connectors
Coating
Masonry
(c)
RC footing beam
Self tapping screw with fender
(a)
Figure 4.35: (a) A masonry wall and (b,c) connector types[131] 145
Index > 4 Applications > 4.3 Applying the strengthening technique 4.3.5.3
Shear strength
The shear strength of a panel can be increased through the application, on the entire masonry surface, of a layer of FRM coating effectively anchored to the wall in order to prevent phenomena of sliding or local detachment of the coating itself from the wall. The shear strength of the strengthened masonry, VRd , can be calculated as the sum of the contribution due to the shear strength of the single masonry wall (frictional mechanism), VRd,m , and that of the FRM coating, VRd,r : VRd = VRd,m + VRd,r
Equation 4.46[53]
The resistant contribution of masonry can be determined with the following expression: VRd,m = l 0 · tm · fvd
Equation 4.47[53]
where: l 0 is the length of the compressed part of the wall; tm is the thickness of the wall; fvd =
fv k γM
is the shear design strength of the masonry evaluated by calculating the average
normal tension σn acting on the compressed part of the section (σn =
NE d l0 ·tm ).
where NE d is the vertical axial action of compression acting on the wall panel. The resistant contribution of strengthening in the last conditions can be calculated using the strut-tie diagram in approximate way. It is hypothesized that following the cracking of the coating, the resultants of the stresses in tension T and compression C are concentrated within two bands arranged along the diagonals of the wall panel (inclination ϑ), having thickness equal to the total thickness of the coating and width br . The simplified model neglects, in favour of safety, the confined effect produced by the vertical loads on the strengthened wall element. The shear design strength VRd,r of the coating is given by the smallest between the resistant contribution provided by the strut VRd,r,C and that provided by the tie VRd,T : VRd,r = min VRd,r,C ; VRd,r,T
Equation 4.48[28]
VRd,r,C = fcm · α · ν · br · tr · cos θ
Equation 4.49[28]
Vr,T = fFtu · α · br · tr · cos θ
Equation 4.50[28]
where: 146
Index > 4 Applications > 4.3 Applying the strengthening technique θ = arctan
h l
is the angle of inclination of the diagonal of the wall panel with respect to the
horizontal; br = 0.25 · h is the width of the strut/tie; l is the width of the wall panel; h is the height of the wall panel; tr is the total thickness of the coating equal to the sum of the thicknesses of each coating layer applied); fcd =
fc k γc
is the cylindrical compressive design strength of the FRM mortar;
ν = 0.5 is a reductive coefficient that takes into account the cracking and the reduced thickness of the strengthening layer; fFtu,d =
fR,3d 3
is the ultimate tensile strength of the FRM mortar;
α = 0.85 is a reductive coefficient that takes into account the uncertainty of the subdivision of the shear between the strut and the tie.
4.3.6
Restoration of fire damaged elements
The restoration and strengthening of existing reinforced concrete buildings can be an alternative to partial or total demolition in cases of fire damage. Before considering the most suitable strengthening technique, it is necessary to calculate the residual capacity of the damaged elements by evaluating the residual resistances of the concrete and of the reinforcement bars’ steel, considering the degree of damage and utilization of the building after repair. After the repair operation, the elements must exhibit sufficient capacity under ordinary conditions and an appropriate fire resistance in the case of a repeated fire. Recently a numerical research has shown that the solution of the HPFRC jacketing is also valid for the restoration of reinforced concrete elements damaged by fire.[135] At the beginning of the research, sections of beams and columns exposed to a standard ISO 834 fire are evaluated[136] to calculate their residual strength. Subsequently, for the evaluation of the adequacy of the strengthening operation, the behaviour of the deteriorated sections is analysed after the repair with high performance fibre-reinforced [135]
Angelo Leonardi, Alberto Meda, and Zila Rinaldi. “Fire-damaged R-C Members Repair With High-Performance
Fibre-Reinforced Jacket”. In: Strain 47.2 (June 2010), pp. 28–35. doi: 10.1111/j.1475-1305.2010.00731.x. European Committee for Standardization. EN 1991-1-2 Eurocode 1: Actions on structures - Part 1-2: General
[136]
actions - Actions on structures exposed to fire. European Committee For Standardization. Rue de Stassart, 36 - B-1050 Brussels: CEN, 2004.
147
Index > 4 Applications > 4.3 Applying the strengthening technique concrete, under usual conditions and under a second fire. Regarding the structural elements of the beam typology, we study a section 300x500 mm reinforced with lower reinforcement 4 ϕ 16 exposed to fire on 3 sides, the upper side in adiabatic conditions. The lowering of strength is of limited entity (about 6%) for the first 60 minutes of exposure to fire. It grows linearly for longer exposure times. After 90, 120 and 180 minutes the strength degradation, it is equal to 15, 28 and 46% respectively of the starting capacity. The bearing capacity of the restored section is always higher than that of the undamaged beginning section. The jacket allows an increase in flexural capacity of about 100% for any duration of fire exposure. In the situation of a beam deteriorated from an exposure to a first fire long 120 minutes and later repaired, it is noticed that the resistant capacity of the restored beam is higher than the original not damaged one. This is valid to a fire of any duration shorter than or equal to 120 minutes. To widen the tests also to the cases of elements subjected to eccentric axial load it is also studied a sufficient significant number of columns of section 300x500 mm reinforced with 4 ϕ 16 per side in the assumption of exposure to the fire on all 4 sides. At deterioration finished, it is supposed to restore the section with a HPFRC jacket of 40 mm thick implemented on 4 sides. An important increase in the bearing capacity of the strengthened column is noted when compared to that of beginning one, damaged or not. Similarly to how it is done for the beam, the strength of the restored section is evaluated in case of exposure to a second fire on the 4 sides. The results of the simulations make it possible to affirm that the solution of jacketing in HPFRC is valid to repair elements in reinforced concrete deteriorated by fires, increasing considerably the capacity of beams and columns and post repair results equally effective speaking of performance in cases of damage from second fire.
148
Chapter 5
Conclusions 5.1
General conclusions
In this thesis, the technique of reinforcement with HPFRC of structural elements was analysed, entering into the details of the characteristics of the material, matrix, fibres and the fibre-matrix interface. In addition, the mechanical properties of the reinforcing composite, its compression and tensile behaviour with experimental characterization tests have been presented. Direct tensile tests, indirect test of brazilian splitting, bending on 3 and 4 points, Wedge splitting test and Double Edge Wedge splitting test have been described. A series of direct tensile tests on dog-bone like specimens and numerous 3 point bending tests on notched specimens were carried out in the laboratory of material testings at the University of Bergamo. Behaviour at high temperatures was illustrated and a reseach in literature was done about the characterization of the adherence or bonding between the HPFRC strengthening material and the traditional plain concrete by tests on jacketed specimens and specific tests for the adherence. Simplified models were examined, the rigid-plastic one and the linear elastic model. Afterwards, in the chapter 4 Applications, the application aspects of the technique were discussed. Various studies and researches were shown which demonstrated the validity of the strengthening solution. The operational aspects for the making of the strengthening in HPFRC, from the design and preparation of the support to the casting of the jacket, were all studied extensively. Next, specific details of the strengthening of slabs, beams, columns, beam-column nodes and masonry were analysed. For each of the structural elements were indicated the methods of design, execution and control of the strengthening with high-performance fibre-reinforced concrete jacket. In the end it was studied also the intervention of strengthening with HPFRC of elements damaged 149
Index > 5 Conclusions > 5.2 Suggestions on future studies by the fire. From numerous studies cited it emerges clearly that the strengthening of structural elements with HPFRC material is an efficient technique for seismic consolidation and adjustments.
5.2
Suggestions on future studies
It is suggested to carry future studies on solutions to increase or optimise the adherence/bonding between HPFRC material and substrate in traditional plain concrete, with or without connectors, so as to be able to guarantee in time and under stress, the strengthening effect of the jacket on the strengthened structural element.
150
Glossary adherence xv, xvi, 37, 59, 60, 62–66, 70, 81, brick 145 82, 94, 100, 137, 144, 149, 150
bricks 143–145
adherences 62
bridging xv, 34
adhesion 42, 82, 112
brush 64
adhesive 48
bypass 86
adhesives 82 aggregate 33, 46, 47, 73
carbon 30, 35–38, 58
aggregates 46
caseback xxii, 96, 103, 104
alkali 41
cellulose 35, 38
alkaline 37
chiseling 81
anchor 85
clamps 48
anchorage 37, 42, 121, 122, 131, 145
clean 85, 99
anchored 29, 61, 122, 145, 146
cleaning 62, 64
anchoring 99
coating 142–147
anisotropic 41, 70
coatings 141–143, 145
arm 138
compression-flexure 71, 108, 115 concrete-and-masonry 83, 90
beams 55, 60, 61, 83, 86, 87, 90
core 84, 107
Bergamo 48, 54, 149
corroded 114
Bernoulli 97, 100
corrosion xvi, 30, 112–114
bilinear 72, 73
crack xv, 61
bottle 98
cracked 70, 72, 73, 94, 132, 133, 140
box 82, 141
cracking 35, 41, 43, 46, 50, 66, 74, 94–96, 111,
braced 98
125
bracing 141
cracks 61
bracings 142
crystallization 42
brazilian xv, 48, 49, 51, 149
crystals 41, 42 151
curbs 84, 88, 89 deck 84, 85, 87–90 decks 84 degradation 93, 148 deteriorated 85, 114, 147, 148
harmonic 82, 114 hinge 60, 61, 126 hinges 63, 121 hooked 36 hydrowashing 82, 98 hysteresis 126
deterioration 92, 125, 126, 143, 148 ductile 37, 80, 89, 90, 97, 121, 123, 126
instrumentation xv, 48
ductility 35, 52, 55, 69, 71, 93, 94, 99, 108, interaxes 112 iterative xvii, 99, 101, 103, 115, 132, 134 111, 113, 119–121, 123 earthquakes 29, 120, 122 electrowelded 82, 84, 86, 88, 99, 114, 115 epoxy 48, 63, 85, 98
Kevlar 37, 38 laboratory vii, xxvii, 48, 54, 57, 79, 149 laws 77, 126
errors 58 ettringite 41
masonry 82, 83, 90, 140, 143–146
Euler 97
maturation 64 matured 46, 47
filament 41
mechanical xix, 31, 37–40, 45, 58, 79, 84, 98,
filaments 38, 42
143, 149
fire 147, 148
mechanics 42, 131
fires 148
microstructure 41, 42
floors 33
mortar 142–145, 147
formwork 98, 115
MSSTM 131, 135, 140
formworks 82, 97, 98 frame xvi, xvii, 29, 66, 95, 96, 120, 121, 130
Navier 100
frames 122
nebulisation 145
framework 35, 94–96, 111, 125
neoprene 66
frameworks 46, 126
nominal 47, 80 norm 100
glass 34, 35, 37, 38, 41, 141
norms 78, 79, 94, 105, 124, 139, 142
grinder 144
nylon 34, 38
groove 56, 57 panel 84, 121–126, 130–132, 139, 140, 146, hammer 62, 144
147
hardening xvi, 35, 41, 46, 54, 55, 58, 61, 66, panels 145 67, 71, 72, 75
patent 33 152
pinching 126
sandblasting 60, 62, 64, 81, 98
plaque 31
scarification 81, 85, 98
plateau 51, 144
self-tapping 145
Poisson 37
Sirtoli 48, 54
polyamide 38
slab 84, 85, 87, 89, 90, 99
polyamides 36
slabs xvi, 34, 41, 86, 88–90
polyester 36, 38
softening xvi, 34, 46, 51, 58, 62, 66, 69, 70, 72,
polyethylene 36, 38
74, 75, 89, 133
polymeric 141
SSTM xvii, 133, 135
polypropylene 34–38
strut xvii, 132–135, 146, 147
polystyrene xvi, 91, 92
struts 51, 107, 108
polyvinyl 36, 38 polyvinylic 35 portlandite 41 pour 126 pourable 82, 96, 98
tension-flexure 71 thixotropic 82, 97, 98, 136, 137 tie xvii, 132, 133, 146, 147 ties 132
pouring 82, 85, 115
tortuosity 46
prefabricated 33
transducers 57, 61
primer 63
trowel 82, 98
pseudo 35
uniaxial xvi, 41, 47, 50, 73
PSLM 131, 135, 139, 140 pull-off 58, 111 research 33, 50, 147 researches 82, 92, 122, 143, 149 retrofit 30 sandblasted 65
wall 146 walls 85, 90, 141–143 waterproof 90 waterproofing 143 welded 61 wooden 83, 85, 88–90
153
154
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